As physicalists there is no bottom up or top down. The mental process of learning 2+2=4 doesn’t cause the physical process or vice versa. They are different ways of talking about the exact same thing. Mental processes don’t ’have Physical effects’, they just flat out are physical processes.

So of course ideas and thoughts can ‘cause changes in our bodies’, they are changes in our bodies.

Similarly when you talk about computers and software, bear in mind that software is a physical phenomenon. It exists in the computer as a physical pattern of electrical charges in memory circuits. It has physical effects in the system because it is physical.