Rock Connection?

Yesterday, I had a conversation about Caesarea Philippi. Picture a large rock cliff, a cave with water streaming out of the rock, a pagan temple, and the gates of the underworld. So, it's been on my mind. Today, reading I Corinthians 10 it came to mind again. Hear this:

¹For I do not want you to be ignorant of the fact, brothers, that our forefathers were all under the cloud and that they all passed through the sea. ²They were all baptized into Moses in the cloud and in the sea. ³They all ate the same spiritual food ⁴and drank the same spiritual drink; for they drank from the spiritual rock that accompanied them, and that rock was Christ. ⁵Nevertheless, God was not pleased with most of them; their bodies were scattered over the desert.

Moses struck a rock (he should have just spoken), water came out, and Israel was being established. Jesus is at a place where water is coming out of a rock and speaks of establishing his movement. Also, at some point he speaks of streams of living water flowing from a person. Paul, in 1 Corinthians, calls Jesus the rock from which water flowed. Paul is reminding us of the Exodus. Is Jesus as well? Is Paul referring to the Philippi event too? These seem to be some interesting connections to ponder.