Leaky Roof

One of the older mobile homes had a small tear in it’s roof. I got some elasticized/rubberized paint to put over the entire roof, but it rained hard for a few days. After the rain stopped, I got a broom & pushed the water off the roof in a couple areas where it was puddling, to expedite the drying out, so I could paint. When I came back a few hours later, water had seeped out of where the tear was and water was again puddled on the roof.

I would like to repair the roof, but an now concerned about trapping water between the roof and the ceiling. I am wondering if would just be easier at this point to open the tear as much as is necessary so the water can evaporate

(weather permitting). Any advice would be appreciated.