highlights plus all over color (at home)

First let me say I'm not a pro, so if someone else pops along who is, listen to them!  The first thing you should do is test strand. Especially if you are dyeing over highlights (by being lighter, they may pick up shades in the ash color...I don't know how light your highlights are, if they are not as light as blonde, it may not be a problem).  You would do the all over color first, then test strand again before doing your highlights (it is a new kit for you, so you need to make sure they won't come out orange or anything, and it will help you time it right). If afterwards your highlights still come out too blonde, you may not want to put the color over them for the reason I just mentioned.  You don't know what the base color is in over the counter dyes, so all we know is that your dye is ash.  That could mean it has a green base, or it could mean a violet base.  If it were violet that would be okay over blonde highlights (if they came out too light, it would make them more ashy and counter yellow), but you wouldn't want to use it if it were green, because then they may get a greenish cast.  Your stylist probably uses a toner, which is a product you'd have to buy at a Sally or other beauty supply shop.  If you test strand your highlights, you should be able to avoid needed to do anything else to them (if your test strand never comes out right, you may need a different kit).

Since you are new to this, let me also mention not to mix your dye with your developer until you are about to use it.  To test strand, only mix a tiny amount and keep the rest separate from each other so it won't be finished with its chemical reaction by the time you get it on your hair.