Do you wash your face with a cleanser after using a face mask?

For the last one month, whatever face mask I am using, after the allotted time, like 15-20 minutes, I have been washing off the mask with a cleanser instead of rinsing off with only water.

I am scared of the mask residue specially cleansing or purifying ones because they are strong) what the long term affect might be. Also how the leftover residue would interact with moisturizer or block pores or cause breakout or whatever.

 Even home made face masks like juice or aspirin, washing it off with cleansers so it neutralizes the ph level (these juice and aspirin masks can be quite acidic) and also makes my skin less sensitive to sun (specially if I am going out, never go out in the sun with residue of acidic mask)

Some may argue that washing off face mask will limit the ability of the mask for work after the allotted time. That is say, you apply a purifying mask, keep it on for 15 minutes, wash it off with cleanser, the mask is no longer purifying your skin. If you had washed it off with only water, it would; have. So you think you're getting more/better result? In my opinion that is just wrong. Because masks are not designed to work for a longer period of time. 5-20 minutes is all you need. So if you're washing your mask off with only water and happy with it, no problem. But if you experience redness, rash or even breakout after applying face masks. try it. Wash it off using a mild cleanser. It is a safer and much sanitary option