What does levels of raging spirit do?

The tool tip doesn't show any changes between levels

When you look at the stats (not the tool tip you are talking about I think), one thing to keep in mind, the minions have to be summoned in order for values to be displayed. So in town you won't see values of any minions. And outside of town you will have to summon your SrS before you can see any stats.

For SrS their life improves. I am sure their damage increases as well, but I cannot remember if I have seen the damage numbers or not. It could be possible that they are not displayed. But I am not sure.

Oh I just read your post again. You said tool tip. Are you hovering over the gem to check? I was talking about, the arrow on the right side of the skill. Do you know where you have the - and + signs to summon more or less of permanent summons? Right of these there is an arrow pointing to the right. When you click it you can see more details for that minion. For Skeletal Arsonists for example you have a page with "Basic Attack" or one for the explode minion skill. There you can see more stats.