I'm not sure if I understand this correctly.

The way it reads is, if I increase it's strength by four I can only break subroutines on strength four ice, not ice up to strength four.

Have I got this wrong?

nope, you are correct. it can only break IC with strength equal to its own. If Atman is STR 3, it can only break STR 3 IC, not STR 0, 1, or 2.

Edit: in the future, you're sure to get more responses from people on questions like this in the rules forum.

I realized I'd put it in the wrong section after posting, so thanks for the reply.