I have some experience in the past promoting my own services, apps,etc on Twitter. I've been able to build up a pretty good following of around 84.8K followers at the moment. I'm not bragging though because I know a lot of those followers are not targeted because of some mistakes I've done before. But I have been able to correct those mistakes and have very targeted followers now. I used to have 100K+ untargeted followers but I have been able to bring it down to 84.8K followers whose majority is targeted. It took a lot of work and I've been able to learn a lot of things on the way.
You will need to have a structured plan on how you will promote your mobile app to your followers. You can't just promote it right out of nowhere just when you're going to launch. Instead give them some kind of value. Understand your potential users and what is of value to them.
I can't stress enough how you need to be getting targeted followers who really care. I know it's not possible to have 100% targeted followers. But you need to try your best to have the followers who actually care and understand your niche. There a really simple way to do that and that's to only( or at least 80% of the time) tweet about things that are related and of value to your niche market. You could write a few very valuable blog posts and post that on your Twitter. I found that just promoting your product on Twitter is not enough and you could be turned off when you finally announce your launch to your followers and it just doesn't get the results you were hoping for. So don't rely on it too much.
What worked for me is turning those Twitter followers to email subscribers. So what you do is give free high quality value to your followers through excellent valuable blog posts, valuable free short ebooks, etc. Your offering could be anything but just make sure that it's really valuable to your niche market. Now you need to collect their email in exchange of the value you're giving them for free(you can do this using services like Mailchimp,etc). So through this you will have built up an email list of people who are really interested in what you are offering. This is of lot more value than just having the Twitter followers. You can still tweet your launch to them but now you also have a highly valuable email list of people who are more likely to purchase. This way you've filtered your Twitter followers and captured emails from the cream of the crop!
There are a lot more detailed and highly valuable lessons I've learned and I'd be happy to go in detail and answer any question you have through a call.