People used to burn the basins for two reasons:
1) They like to troll and pretend that the boss already appeared to make you more skeptical and stop checking it.
2) When at least 1 basin is burned and Shlorg will appear, he will be in his mortal version - Weakened Shlorg. So they will safe about 30 seconds.
In my opinion, it doesn't make any sense to set fire to the basins before the boss appear, mostly people who create their own theories to believe in them used to do this.
And of course it is not possible, to trigger Shlorg's spawn in any way.
PS. I have no idea if burning basins have any influence on a floor reset, but from my own experience Shlorg used to appear when basins don not burn.