Why are queries causing spill to tempdb?
There's several different questions in here:

Q: Why weren't the queries spilling before?

They were, but SQL Server Management Studio didn't surface this as a clear error prior to SQL 2012. It's a great example of why when you're doing performance tuning, you have to go deeper than the graphical execution plan.

Q: Why do queries spill to disk?

Because SQL Server didn't grant them enough memory to complete their operations. Perhaps the execution plan underestimated the amount of memory required, or perhaps the box is under memory pressure, or they're just big queries. (Remember, SQL Server uses memory for three things - caching raw data pages, caching execution plans, and workspace for queries. That workspace memory ends up being fairly small.)

Q: How can I reduce spills?

By writing sargable T-SQL statements, having up-to-date statistics, putting enough memory in the server, building the right indexes, and interpreting the execution plans when things don't work out the way you expected. Check out Grant Fritchey's book SQL Server Query Performance Tuning for detailed explanations of all of those.