It doesn't matter when the tuition was billed or what the 1098-T says. What matters is when was the tuition was actually PAID. If the spring 2017 tuition was paid in 2016, it was deductible (or counted toward the education credit) in 2016.
For example: If it wasn't paid until 2017, it gets reported on your 2017 tax return. That's one of the purposes of a December billing, to give the taxpayer the option of paying in 2016 or 2017.