Imprisoned opposition politician and founder of the Anti-Corruption Foundation Alexei Navalny learned about the announced mobilization at a court hearing in Kovrov, where his lawsuits against his penal colony are heard. Mediazona quotes his response to Putin's and Shoigu’s statements from earlier today.
“There's one thing I can't fathom. The Army has one million troops. The Russian Guard has 350,000 people; the Ministry of the Interior has another 1.5-2 million, and that's not counting the penitentiary system. Why would they draft civilians? As a result, five million dodgers will be running around the country. And one million cops will be chasing them to get them to enlist. ... Take ordinary workers from the town of Kovrov, for instance, guys in their early thirties. They’ll be mobilized in no time and end up killed somewhere outside Kherson. It's horrifying. I don’t think they will mobilize many Moscow residents. If you take away 50,000 Muscovites, their relatives will walk out in protest in a 150,000-strong rally on the next day.”
President Vladimir Putin announced mobilization in Russia on September 21. The presidential decree is available on the Kremlin's website. Minister of Defense Sergei Shoigu followed up on Putin's address with a statement that mentioned mentions plans of mobilizing 300,000 reserve soldiers and officers.
For now, there is no telling if Russia will ban international travel for all of its nationals liable for military service. The Russian law on mobilization says that all individuals liable for military duty “are prohibited from leaving their place of residence upon the announcement of mobilization without the authorization from military enlistment offices, or federal executive authorities in charge of the reserve.” You may find more information here.