If your phone not support Cell ID API 4.2+, Cellmapper App not allow turn screen off. When you using old app on phone, cell screen won't updating when screen is off. That's why app keep screen on.
App have also feature called "Blank Scree" what you can find on Main Menu. Using this feature on phone what have AMOLED-screen reduce battery drain.
Also if you record CDMA network, screen not allow turn off.
You can check API 4.2+ supported phones on Tested Phone page. Mostly Android 8 and newer phones support API 4.2+. Qualcomm Snapdragon (except Samsung Phones) phones after Android 7+ support API 4+2.