I have just tried to book the flight to Istanbul from a couple of random cities of Russia for the experiment and had no problem.
Also the limited ‘conspription’ involves around 1% of ROTC and and active reserves. Not enough to clog airports even if they wanted to.
Total reserves (Naval, AF, and Army) are around 2-million for Russia. The number that gets discussed is 300,000 for this activation. My humble guess...most all of the 300,000 are Army reservists, who fall into the infantry, logistics and tanker occupations.
The airline ticket business reflects routes to countries that have friendly visa-situations with Russia.
It is conceivable that when they start calling for activation orders...that 5,000 to 10,000 of this group have already left the country. I doubt if anyone is really tracking those who left Russia.