Why output voltage of power adaptor is increasing when more load is applied instead of dropping?
That AliExpress page for the mains power adapter says the seller's specification for the output voltage is 5V +/- 5%. Even your 5.4V measurement is higher than that specification, without mentioning the 6.7V measurement!


  This may damage other modules


Agreed. It might be interesting to see the output voltage on an oscilloscope, in case your multimeter is being confused by (for example) increasing AC ripple superimposed on a DC voltage etc. However, whatever is happening to that 5V output under high load, I would not risk using that mains power adapter.


  What may cause this


Faulty power adapter - either a faulty unit, or a faulty design. Unless you open the unit (obviously this is a risk due to the high voltages inside!), then reverse engineer the design, and then make appropriate measurements to find the actual root cause, then I don't see how you can be sure of the internal reason for that behaviour.


  how to deal with it


Either open the power supply (and therefore lose any warranty and incur the risk of working near high voltages), find the cause of the problem yourself and then design a fix - which I don't recommend, but I don't know your level of skill, what safety training you have received, or whether this is something that you might want to do; or replace the mains power supply with one from a more trustworthy supplier.

FYI even for my hobby projects, I never buy no-name power supplies from AliExpress, eBay etc. due to exactly these risks. The possibility of them damaging the rest of the project is just too high for me. :-(