My guess is the "rubbery" material is a vapor barrier to protect whatever wood products are under the "concrete". 

There are vapor barriers that are much tougher than regular felt paper and Tyvek.

if so, ask for closure reports for old tanks(3) check condition of spill buckets and make sure they are monitored. if not, should collect samples from around those structures. they often get dinked by snowplows and vapors may escape then condense into soil.(4) has property always been on public sewer since it operated as gas station. if not, did they perform auto repair?

I find it useful to have a couple people that will remove old flooring (carpet, vinyl, etc), clean out crawl spaces, repair insulation, lay down vapor barrier, haul off junk, remove fencing, paint decks, low skill landscaping, etc.The best method I've found is posting free stuff (used appliances, old fencing, and other stuff) on CL, then identifying the good character workers to do other work for $15 hour. 

Buy a paint respirator with organic vapor cartridges.

The typical configuration for oil finishes is P95 particulate  prefilters fastened over organic vapor cartridges.

Remember when we went out of our way to make laws about flavored vaping because of some contaminated weed vapors?

The other is they now want a vapor barrier installed in the floor but these are older model trailers “as is” and we haven’t had an issue with mold or moisture.

Stop getting the vapors and answer the questions.

Anyway, you MIGHT (or might not) be able to get away with a vapor mitigation system to treat the indoor air issue.