Thanks for that! The wording of it brings up new questions though.
"they have, or were last granted permission to stay in the UK as a Tier 4 migrant" implies that as long as my last permission to come to the UK was Tier 4, these rules will be in effect. So if my current visa expires and I go back to the US, and then try to apply for jobs here at a later date, they still won't have to do the resident labour market test?
The first part of that 28.8 wording states -
28.8
You do not have to conduct a resident labour market test if a migrant you want to sponsor is applying for Tier 2 (General) leave in the UK and has, or was last granted leave to enter, or to stay in the UK under one of the following:It's for those who are switching (in the UK) with a valid Tier 4 visa. If your visa has expired, then you can't apply "in the UK" and the company will have to carry out a RMLT.
It's a reward (for the want of a better word) for those that studied in the UK, have a valid Tier 4 visa and have a company that want to sponsor them in a graduate job. This removal of RMLT for valid Tier 4 visa holders, was in the new rules. It's all part of their 'keeping the best and brightest students'. The company uses an unrestricted CoS (no limit to how many the UK will give out) meets the salary requirement and then the Tier 4 visa holder can switch (in country).
A new visa automatically cancels out the old visa, as only 1 visa can be held at any one time. If their last visa was Tier 4 then the company doesn't need to carry out a RMLT, but if it wasn't, then they do. i.e. Student to points based dependant, now wants a Tier2 (General) = the company need to carry out a RMLT and use a restricted CoS (limited numbers per year) as the migrant didn't have their last leave as a Tier 4 and looking under the "switching" rules also, shows that they must apply from outside the UK.
If your Tier 4 expires and you apply for jobs in the UK from the US, the company will have to carry out a RMLT. You would need a restricted CoS.