You say "I also looked and it seems the IRS does allow reimbursement to occur within the first 3 months on the next year to count towards the previous year, similar to IRA contributions". Do you have a reference for that.
I believe your employer is doing it right. By law your employer can only give you $5250 maximum, tax free, per year. It goes by the year of the reimbursement, not the year of the education. I believe the 3 month rule, you saw, only has to do with whether you qualify for a tuition credit or not.
If you got more than $5250, in a calendar year, the amount above $5250 is included in box 1 of your w-2, as income. Since you have essentially paid tax on that part, it is considered your after tax money and that amount can be used to claim the tuition credit, for the year the tuition was paid. .
