I bought some Tulammo at you know where mart and a lady next to me said "Oh, steel core, you can't shoot that at a range." I said its steel case, not steel core and I shoot out in the woods.
AFAIK the bullets in recent-production Tulammo use mild steel
jackets with a thin bonded copper coating. This type of bullet construction is known as "bi-metal", but this term is often confused or conflated with true steel-core construction.
The main reason for restrictions on bi-metal
or steel-core bullets at shooting ranges is that they chew up steel target hangers and steel-plate targets much faster than traditional copper-jacketed or non-jacketed lead bullets do. Another significant concern is that they tend to ricochet more severely, which poses an increased risk of injuries to people on the firing line, and a greater fire danger, particularly if the backstop contains lots of hard objects (such as small igneous rocks) that may create sparks.
Are ricochets and fires a particular concern at your backyard firing range? If you live in an arid climate with rocky topography, they could be. At any rate, I would NOT use bi-metal Tulammo if you're shooting at steel plates, setting aside the ricochet risks; you'll simply wear the targets out faster, and possibly by blowing holes straight through them.
There's also been much wailing and gnashing of teeth on various gun forums about the possibility of premature barrel wear from the steel jackets; however, the general consensus is that (a) it's mostly a concern if you do repeated rapid-fire mag dumps through a hot barrel, something few shooters have the budget or desire to do frequently; (b) most barrels will still last many thousands of rounds either way; and (c) even if you DO manage to wear the barrel out, you'll probably still come out ahead if you factor in the cost savings from the cheaper ammo.