You... really have no idea how to read that graph, do you? Or what a lagging indicator is, I'm guessing.
The fact is - we can see the rate of change of the sea levels start changing in the mid-90s, though the graph you're using compresses the Y-axis to minimize how obvious that is (deliberately, I'd say, given the source).
Which, given its a lagging indicator of the result of rising CO2, makes sense it would happen after.
So, even accounting for the dishonesty of the presentation (and make no mistake, it's VERY dishonest) it actually demonstrates the exact opposite of what you claim.