It doesn't matter when the the tuition was billed or what the 1098-T says. What matters is when was the tuition was actually PAID. If the spring 2014 tuition was paid in 2013, it was deductible (or counted toward the ed credit) in 2013.
If it wasn't paid until 2014, it gets reported on your 2014 tax return. That's one of the purposes of a December billing, to give the taxpayer the option of paying in 2013 or 2014.
