Updating values authenticated by Merkle Tree
What do you mean that you keep the root of the merkle tree locally? Is the merkle tree signed?

If i understand what you are saying correctly, then the server can choose not to display to the public the changes you have made and keep presenting the merkle tree for the values before you updated them.

Even if you sign the merkle tree the server can still do that. However it cannot arbitrarily change the files. Only use old values.