Does anybody else remember the fact that Caroline sent Klaus an invite and that is why he arrived on time. He was already on his way.
I think the fact that she willingly sent him an invite says far more than him proclaiming he will be her last love. We have all known for a while that Klaus cares about/loves Caroline. While what Klaroline shippers have been waiting for is Caroline to make her move.
Well guess what? She did. There as no reason she would send Klaus the invite. Nobody was plotting to hurt Klaus. Nobody was plotting to use Klaus. At least not when she sent the invite.
Then there is the fact that Klaus is a thousand year old hybrid. Thousan year old hybrids have better things to do then attend a trivial high school graduation. For instance, they may have a city to take over.
And yet Klaus takes time to actually travel back to Mystic Falls because Caroline invited him. He knew this was the opening he had been waiting for. This was the first new step to a new part of their journey.
In my opinion I think that is why he let Tyler come back. He let Tyler come back because he knows that some part of Caroline wants Klaus around.
We also can’t forget Caroline’s giant smile when she realized Klaus had actually shown up or the fact that she joked with him.