ASINspector Pro will almost always update automatically. This is one of the advantages of being a Chrome Extension. From time to time this doesn't happen in certain circumstances.
You can always check what version you are in by placing your mouse pointer over the logo in the left corner of the screen.
If you don't have the most current version. (Check with support on this or just follow the next procedure.)
Go to your Extensions window in Google Chrome. You can get there by clicking the 3 Dots on the right hand side of the address bar. Then click "More Tools" then click "Extensions".
You will then be taken to the Extensions screen where you now can put a check mark by clicking in the box entitled "Developer Mode." Click the button that will appear that says "Update extensions now". You can close this window and you should have the most current ASINspector Pro version now.