Refresh Current Page After Save & Keep Working

1. Use a form rule to copy the temp id to the Asset ID on save. Below is an image of an example that I have working in an app where the "Rate ID (Rate Type)" is the key field. I like this option because you can use the native save buttons.
   
   
2. Use an API action button to copy the value from the temp id to the Asset ID. This would be the approach you originally started with but with the addition of the API. It would require the user to use this button in order for the key to update. Below is the button I'd create if I were doing this myself. (Note the key field id '7' on line 5 would need to be updated with the id for the Asset ID, the [Temp ID] for your field name, as well as the apptoken on the next line).

var text NEW =
URLRoot() & "db/" & Dbid() &
"?a=API_EditRecord" &
"&rid=%%rid%%" &
"&_fid_7=" & URLEncode([Temp ID]) &
"&apptoken=xxxxxxxxxxxxxxxxxxxxxxxxxxxx" & 
"&rdr=" & URLEncode(URLRoot() & "db/" & Dbid() & "?a=er&rid=") & "%%rid%%";

var text SAVE = 
URLRoot() & "db/" & Dbid() &
"?a=er&rid=" & [Record ID#];

var text URL = If(IsNull([Record ID#]),$NEW,$SAVE);

"<a class='btn btn-md btn-success SaveBeforeNavigating' style='color:white; text-decoration:none;' data-replaceRid=true href='" & $URL & "'>Save & Keep Working</a>"​

If you want to learn more about action buttons I have a free toolbox called the Action Button Toolbox.