Collaborative proofing - client website shows 'custom order' rather than chronological order

OK, here's how it works. The client always sees whatever is set as the current Custom Order in the cloud ecosystem, if one has been set. That could have been set in any of the Lightroom "cloud" apps, or even Lightroom Classic if that has been synced to the cloud, as the custom order does sync across the system. So, whatever was the latest custom order set is the order that a shared album will be viewed by the client.

Ideally, the client should have their own display ordering capabilities, but in the absence of that the owner needs to ensure that the order reflects what they want the client to see. That has been made quite easy by using the browser-based LrWeb app (login using your Adobe ID credentials at lightroom.adobe.com), then select the album in question and click on the "Display" icon at the bottom of the grid (looks like an artist's palette). When the Display dialog initally appears it'll probably be just a single line, so click on the up arrow at the right to expand it. Then you'll see the option to "Reorder By" near the bottom, together with a drop down list of various sort orders. Clicking on one of these will reset the current Custom Order to whatever you have selected, thus enabling your clients to view the album the way you want it to be seen.