Stranded wire gauge too small for push-in connector(USA)
This cannot be a problem

The connectors are listed for a wide range of solid and stranded wire.  A wider range, in fact, than you are allowed to use inside fixtures, which must be no smaller than #18 for mains voltage - that's according to UL.  

Now, if the fixture is not UL listed (or other NRTL), don't use it.  Especially if it's one of those foreign jobs obtained off Alibaba, AliExpress, eBay or Amazon.  Those are predominantly dangerous junk, and obviously they have not the slightest regard for our safety codes.  CE and CCC are not proper testing labs such as UL.  

If it is a fixture of your own construction, that is between you and the AHJ, but you will at least need to retrofit the internal 120/240V wires to #18 or larger.