As far as I know it should run ok on the Tula stuff. I think most of the fears with steel cased ammo is in the Mini-30 where it's rumored that the steel cased berdan primed ammo is responsible for broken firing pins. Personally I won't run steel cased ammo in my Mini-14 because I reload. You might want to keep in mind that Ruger doesn't seem to approve of the steel cased Russian ammo.
Originally Posted by Ruger Manual
The Mini-14 Ranch and Mini Thirty Rifles are designed to use either standardized U.S. military, or factory loaded sporting cartridges manufactured in accordance with U.S. industry practice. Always be careful to ensure you are using the correct ammunition for your rifle. See “Ammunition Notice” & “Warning - Ammunition,” below.