You should have nothing to worry about as far as compatibility is concerned.
Let the wood dry overnight ...?
In actual fact it's usually a good idea to wait for this type of thing to fully dry even if the instructions say otherwise.
Given the time gap between you asking and reading an Answer you've almost certainly given it ample time!
For some added context, "wood conditioner" isn't really a thing. It's merely a marketing name for one of a number of products made to help lessen or prevent blotching in blotch-prone woods and as such it really has little use in any other context. Although it can be used to deliberately make any wood stain more lightly, you can do this in other ways without having to put something on the wood first and then have to wait for it to dry1.
In the past, before these products came on the scene, this same job was accomplished in other ways, e.g. using a thin application of shellac (sometimes referred to as a spitcoat) or glue size (diluted glue). An initial dilute application of varnish or lacquer can also be used, as can a coat of oil if that fits in with the overall finishing regimen. And all of these can still be used for the same purpose, without of course having to buy a specialised product that has no other use in the shop.
Most commercial "wood conditioner" is merely a type of diluted finish, i.e. nothing you couldn't make for yourself in two minutes, but with a huge mark-up on the price considering what's in the container is mostly thinners2.
1 Apply less heavily (most application instructions call for a huge excess to be applied, most of which ends up on the wiping rags and not on the wood!), dilute or thin the stain, wipe off sooner and/or more thoroughly, dampen the wood prior to application. Or buy/mix up a lighter colour to start with and apply it normally.
2 Just like with most "Danish oil", "teak oil" and wiping varnish.