When to reject offers?
When the pay is too low, absolutely or in terms of hours required.
When the employer can't or won't get you a Residence Permit.
When something about the contract, location, housing, etc. is simply unlivable for you.
When you strongly suspect you're going to get abused or ripped off.
Now...what you really need is a Residence Permit (RP), not a Visa. They're often confused, but definitely not the same thing. You generally pick up a new (not a renewal) Visa in your home country, or an intermediate third country, not China. A Visa gets you into China legally, but the RP is what actually lets you live and work in China.
Your degree status has no bearing on a Visa..but it definitely DOES have on applying for an RP.
On the case you cite...you should be fine. If the school can definitely get you an RP, and takes care of you while it processes, there should be no trouble at all.
When you enter China for a job, once you come in on your Visa you have 30 days to apply for an RP. As long as you're within this period, or the school can show that your RP is well in process, you should have no problems coming to teach September 1.
That said, be aware that things like offering jobs to more foreign teachers than they need and then withdrawing offers to the overage, or suddenly withdrawing your offer because they found another foreigner who demonstrates more stupidity than you do (ie by agreeing to take a lower salary), are pretty common in China...even in the face of a signed contract with you.
Be aware that in China, contracts are simply amusing novelties, sort of like party favors. Employers can and do violate or ignore or unilaterally change them with impunity, especially at someplace other than a SAFEA-regulated university. Chinese employers will get jiggy on using your contract to make sure YOU hold up YOUR end of the bargain, but show zero compunction to use it to regulate THEIR behavior. However, pasting Chinese contract sheets together for that plush 2-ply comfort, then rolling them tightly around a short cardboard core, at least makes them of some possible utility in the bathroom.
And be aware that in China, many schools' Foreign Affairs Officer (FAO), whose primary job it is to get you the documents you require, will in fact know next to nothing about actually getting you those documents. But since revealing this ignorance (or trying to eliminate it) would be too embarrassing for the FAO, they will say just about anything that pops into their heads, and/or make a total bollix of your applications, requiring extra time and hassle.
TIFC ("This Is Fucking China"). Coming here is always riskier than staying home.
Take some comfort from the fact that in most cases, things tend to come close enough to working out.