In Russia swastika was considered an "Asian symbol" at the time. During Russian civil war, swastika was adopted as a symbol of Kalmyk units of the South-East front of the Red Army.
Here is the decree, establishing it as an armbadge:
Here is the actual armbadge:
Swastika is called "«ЛЮНГТН» sign" in the description, it is unclear what the acronym stands for. The South-East front used it as an award badge as well:
The Whites also used the symbol extensively. The Asian Cavalry Division, a Cossack formation headed by baron von Ungern-Sternberg who captured the Mongol capital Urga, had Mongol and Tibetan units. Austrian by birth, Ungern himself married a Mongol princess and adopted Mongolian clothing style.
His superior, ataman Semeonov, also reported (by General Leutnant K.V. Sakharov) to wear shoulder badges with "the sign of Mongolian Suuvastika". Osednovsky reports that the Mongolian formations of the division used shoulder badges with swastika.
It is also reported that Ungern was awarded with a ring with swastika, allegedly beloged to Chengis Khan.
Ungern's adjutant and division's commandant N.N. Kneazev reports "holy yellow flag with a sign of Chengiz Khan (swastika), which became for the whites and the Mongolian people the symbol of struggle against the Communists".
The French historian Gerson also reports the division to use flags with swastika.
Himself, baron Ungern adopted Buddhism, while still retaining Christianity (he was Luteran). He was a staunch Monarchist and dreamed about restoration of Chenghis Khan empire that would govern both Europe and Asia and prevent revolutions. He also tried to create "Order of military Buddhists", also known as "Order of Buddhist Crusaders".
Since baron Ungern conducted proto-Nazi policy (killinng all Jews and Communists on site), I suspect that his army was in fact the very reason why Hitler has adopted Swastika: there were a lot of White emigrants in Germany at the time, and they could very well influence Hitler who possibly considered Ungern's army as an example.
It is possible, Hitler adopted other his ideas from Ungern's ideology as well: during a discussion with another White officer General Molchanov about what to do with the Jews, Ungern-Sternberg stated that it was necessary to "exterminate the Jews, so that neither men nor women, nor even the seed of this people remain"
Alongside Ungern-Sterberg's aristocratic pride was an ardent
anti-Slavic racism that led him to view all Slavic peoples as
naturally inferior and barbarous to the "superior" Volkdeutsche
(ethnic Germans) like himself.[ 10 ] Ungern-Sternberg believed that it
was the Volkdeutsche nobility of the Russian empire who were the
Herrnvolk ("master race") that kept the empire working, and that if
the Slavic Russians were left on their own that they would inevitably
fall for the tricks of the Jews, whom the anti-Semitic Ungern-Sterberg
saw as his archenemies from his childhood on.[ 10 ]
Dr. Klingenberg, a fellow Baltic German who was close to Ungern
because he was one of the few officers who spoke German as his first
language was a Social Darwinist who believed in the "survival of the
fittest" suggested to Ungern that he be allowed to poison those
wounded and sick soldiers who were "unfit", an idea that Ungern gave
his approval to. Dozens upon dozens of Ungern's sick and wounded
soldiers were poisoned by Dr. Klingenberg, who was so enthusiastic
about killing his patients that many ill soldiers preferred not to
visit the hospital, least they fall victim to Klingenberg.
After the battle, Ungern staged a pogrom against the Russian Jewish
refugees living in Urga as he led his Cossacks against the Jews,
ordering that all Jews be killed as he stated, "in my opinion, the
Jews are not protected by any law". The Mongols, who had no
tradition of anti-Semitism, did not understand why Ungern wanted to
slaughter the Jews, and as Ungern led a Jewish baker named Moshkovich,
renowned for his kindness, away to be hacked to pieces, many ordinary
people were heard to ask "What harm has he done, this good old man?",
only to brushed aside. In Russia, gang rape had always been an
integral part of the pogroms, though usually only men were killed in
pogroms. In the Urga pogrom, gang rape was very common, but this
time women and children were killed as Ungern gave orders to kill
every Jew without regard to age or sex. Prince Togtokh, a Mongol
prince famed as an anti-Chinese guerilla fighter and until then one of
Ungern's strongest allies, had attempted to hide some Jews in his
house that he just reclaimed from the Chinese. Ungern stormed
into Togtokh's house, had the Jews taken out to be beaten to death on
the streets and when Prince Togtokh protested at this violation of the
sacred Mongol law of hospitality, nearly had him hanged. When a
Danish missionary named Olsen protested, Ungern had him tied to a
horse and killed by dragging him through the streets. So many
bodies were left on the streets of Urga that packs of wild dogs
started to devour the dead.
Now one more example of usage of Swastika at the time. There was Swastika symbol on the banknotes of the Russian Provisional Government of 1917:
The swastika is described simply as "geometric ornament" in the official description of the banknotes, but the underlying reason is deeper.
The banknotes were produced from the designs originally intended for Mongolian National Bank. The bank's headquarters were to be located in Petrograd and its banknotes were planned to be printed by the Petrograd Mint.
There are specimens of this currency that remained:
In conclusion, in all the mentioned examples Swastika was intended as an Asian (specifically, Mongolic) symbol.