I will be railing from Vladivostok --> Moscow on the "Rossiya". I found the following information on seat61.com.
Remember that Trans-Siberian trains are 'reservation obligatory'. Every time you step on board a train you must have a confirmed sleeping-berth reservation for that journey on that train on that date - you cannot hop on and off trains spontaneously without a reservation. So if you want to travel from, say, Moscow to Beijing stopping off at Irkutsk you need a ticket/reservation from Moscow to Irkutsk and a second separate ticket/reservation for the train you want to take from Irkutsk to Beijing.
It also reads:
The train stops several times a day, usually only for 10-20 minutes, but you can stretch your legs and take photographs.
I just wanted to verify that of course this means you may hop off/on the train at any station stop, provided you board the same train before it makes way again. I think thats what it means. Perhaps my brain doesn't work properly.