I treat my minis the same way I do my full size roses since they seem to catch all the same things.

I ortho them along with the big ones, since it seems to be the only thing that keeps the aphids at bay.

Not a pro or anything though, so wait and see what others have to say.

Aphids are a real pain, but they are manageable.
I got my information from the book "Backyard problem solver" you can get some good information from it.
There are some good sprays you can buy that are not too strong. Read the label first some bug sprays for roses don't work aphids, so if it says it kills aphids you have a pretty good chance of getting rid of them. There are about a dozen kinds of aphids some sprays work better on one kind than another. What I did was find one that worked for me and keep it stocked.
You can also try lemon rind.
What you do is grate one lemon rind and put it in 2cups of water then pour through a coffee filter. After that put it in a hand held sprayer then add one tea spoon of dish soap (lemon scented is a good idea) and shake it up. Hose off the aphids and wait for about ten minutes and spray the whole bush. Repeat again in about 4 days.

Here is a link that might be useful: Backyard problem solver