Mobile attribition partners (like Appsflyer, Adjust, Branch, ...) help you not only to differentiate organic from non organic users. If you increase UA spend and do UA via different networks (facebook, UAC, ....) you want to splice your non organics so that you can see where they did come from and towards which ad they acted. But this is not for free. You typically will be charged for non organic installs. In fact this cost will reduce your ROAS. If you do UA in territories with low CPI / LTV this cost can be significant in relation to your CPI/LTV (so ROAS might be lowered substantially).
But for the start you could take a different approach:
1) concentrate on ONE UA source AT A TIME (I would recommend to just stick with UA via facebook as a start) for a given interval
2) deduct the installs that the UA source claims in any given interval from all installs (signups) that you track in your database
Now you have a rough ratio between organics and non-organics.
Turn on and off the paid UA for an appropriate interval (say 1 or 2 weeks) so that you can estimate the ARPU/LTV/KPI of a pure organic user of your app.
Of course as you progress and optimize your app the KPIs will change (hopefully for the better). So you need to re-calibrate from time to time.
I'm not sure if the free Appsflyer plan supports it but there is an af_purchase event which is mandatory to at least see the revenue generated by a given user (organic vs non organic). You can use Appsflyer's automatic validation (against your Apple/Google account) or you may send the af_purchase manually (be aware that in that case you should do the validation on your server before your app calls af_purchase or you will see inflated, fraudulent revenues).