Good luck getting that by your DM
If this works hinges on the question if they rule the phasms alternate form ability qualifies for Assume Supernatural Ability. That feat says:
You learn to use a single supernatural ability of another kind of creature while assuming its form through a polymorph self spell or a similar effect.
To quote from @Chemus answer:
Interactions between 3rd and 3.5 form altering abilities are, therefore, to put it in technical terms, an awful mess. This highlights why some players will say that most form altering magic that lets a creature appear to be another to meet the 'polymorph selfspell or a similar effect' metric of the Assume Supernatural Ability feat, and others adhere to only converting the words polymorph self to polymorph.
If your DM decides this is similar enough, it will work. However, there are a lot of differences between alternate form and polymorph self, the major one is this stipulation on Polymorph:
The assumed form can’t have more Hit Dice than your caster level (or the subject’s HD, whichever is lower)
Now, the Shape of Fire as a CR 26 creature has 35 hit dice, and some terrifying special abilities commensurate for a CR 26 threat. A phasm is a CR 7 creature with 15 hit dice. If you consider that the target should not have more hit dice / levels than your current form as an important attribute of a polymorph spell, then these effects are not similar at all. One allows you to change into any CR of target, the other allows you to change into a same or lower CR.
Assume Supernatural Ability then will not work, because you did not assume the Shape of Fire with polymorph or a similar ability. I think this is a quite convincing argument against this working.
But lets assume it works, your DM is up for shenanigans because they can get you into trouble. Then it is not clear how long you retain control over whatever lavawights you create because:
Lavawights are under the command of the shape of fire that created them and remain enslaved until its death.
When your polymorph spell ends afer a few minutes, you revert to your own form, and you are not a shape of fire any more. But you have not died. Maybe that means you still can command them, maybe not. If your DM decides that not, all you have is a costly way to create uncontrolled lavawights.
If the DM decides you can both create them and keep control of them if you revert, you instead have a way to create an unending army of obedient lavawights for the cost of two feats.