That's mostly true. It takes a few centuries for warmth to percolate into the deep ocean and up on the other side to release more CO2. In general the charts show about an 800 year lag from warming to more CO2.
However the current rise in CO2 is manmade. The simplest explanation is that the oceans used to release more CO2 and still would with warming from the Little Ice Age. Instead the oceans are absorbing CO2 net. There is still release of CO2 from the oceans in various seasons and regions. But mostly the oceans have switched to absorbing.
Looking at the same charts showing the lag from warming to CO2 release, they show about 10 ppm of CO2 released for every degree of warming. We currently have about a 120 ppm rise and we certainly have not had 12 degrees of ocean warming to explain that.