For the first 1-2 weeks of the feature, we saw around 8-12k new users everyday, a figure which has obviously since declined but we are still getting a modest 2-3 k new users every day and retention has been alright too.
As for working with a publishers, my experience with Appsolute was generally positive-- they're a small team from what I can tell so the working relationship had been pretty relaxed in terms of requirements and expectations form their side in the months/ weeks leading up to the launch and they were confident form the start that we'd get a good spot from Apple, which we did.
That said, most of the work and initiative had to come from us and in terms of guidance and inputs for how to shape the in-game experience to support monetisation etc, there was practically nothing form their side. I've been working on mobile games for some years (not full-time) so I spent an awful lot of time and effort to try out multiple icons, different creatives, run beta tests through platforms like BetaFamily and Betabound to consistently gauge user-sentiment and improve the game and so on, over a period of 6-8 months.
Most publishers will treat all games the same, which, sadly, in today's mobile-gaming landscape, implies hyper-casual games. We had a far more detailed game (which we are now actually porting to Steam) and we did feel that it was just left own its own and never properly targeted towards the right audience through any promotional activity, PR or even basic ASO.
I don't reckon we could land a feature if we published the app ourselves so for getting it ANY visibility, we do credit the publisher ,and overall, it's been an experience that has given us good confidence to carry on ahead.