"Your coverage was ended" - if your participation in the FSA was terminated prior to September 30th, then yes.
"The HSA was opened automatically, " HSAs are not opened automatically; instead, in most cases your employer helps you sign up for it when you sign up for the HDHP coverage (even if you didn't realize it at the time). But as I noted above, the HSA belongs to you, not the employer, so if you leave the employer you do NOT have to close the HSA - in fact, that's a very expensive thing to do.
The HSA is created per state law. Generally, this is when the first contribution reaches the HSA. This can be important because of another funny HSA rule: you can ask the HSA custodian to reimburse you for medical expenses that were incurred after the HSA was created.
For example, you had a qualifying medical expense on October 1st. Suppose you did not have enough money in the HSA to pay the bill, so you paid it with after-tax dollars at the time. Later, say in February of the following year, you now have enough money in the HSA to pay this bill. At that point, you can call your HSA custodian and ask that the HSA custodian send you ("reimburse") the amount equal to the bill that you paid on October 1st. Since the amount passed through the HSA, you received a tax benefit when the original contribution was made to the HSA, so you, in effect, received a discount on your medical bill.
Note that the IRS does not place a deadline on when you reimburse yourself - it could be years later. The only limit is that the original medical expense had to take place after the HSA was created.
Your plan is the normal plan, to stay under HDHP coverage for the next year. However, as we have seen here at TurboTax, people are sometimes unexpectedly terminated anyway. I wanted you to be prepared if the worst happens.
Note that it does not matter how you happen to be covered by an HDHP to be able to qualify for the testing period (and be able to contribute to the HSA). Thus, if you were laid off but qualified for COBRA coverage, then if the COBRA policy was also an HDHP, then your HSA status would remain the same - the HDHP coverage does not have to be from your employer or any employer (in fact, it could be from your spouse). This may affect your decision to take COBRA after a termination (usually an expensive option), since it would allow you to avoid declaring the excess HSA contributions from the previous year as income and paying penalties.
