That's the difference between signing and ratifying. There's a story that USA's Congress never ratified the end of the war with Europe. A lot of countries voted No to the European referendum. Most of them voted Yes. Ultimately, the citizen should decide when they give up power, and they must repeat it regularly.
Direct democracy in diplomacy and trade negotiation sounds like a really terrible idea. It would just be constant protectionism, xenophobia and probably ruin economic growth and everyone will be the worse of for it. Sometimes giving more people a voice does not result in positive outcomes.