Google determines how a visitor would view your page that comes from its search engine. If your homepage has an amazing article about "cupcakes" and a user searches Google for "cupcakes", Google will want to send them to your page that has an amazing article about "cupcakes". It will not want to send them to a page that requests for them to download your app.
In other words, if you're trying to rank your site for certain keywords, it's not going to work very well if you offer a splash download page. Google wants to send users to content rich pages.
Googlebot and organic search traffic visitors visit your page very similarly to how someone would visit your page if they typed your domain into their browser. Googlebot, organic traffic, and direct traffic are all coming from a non-http_referrer. In other words, Googlebot and the traffic coming from Google will likely see your splash page.
If you want to fix this issue, you need to identity what traffic is not coming from Google. One way to do this would be through logging a cookie, or logging the user's IP address. When a user comes to your site, and has already been there, then it is ok to show the splash page. But in terms of showing a splash page directly to organic traffic first time visitors, I don't think Google is going to like that page very much.