Was the old BB a loose-ball unit with steel cups? Because of the way they were adjusted, they could be machined to turn pretty easily when threading them in. The newer cartridge units with aluminum cups will fit tighter because the aluminum is expected to deform a little on installation, and all of the threads need to support the torque. Better that they start out a little too snug than too loose.

That said, if it doesn't feel right going in, some caution is a good thing.