For the url https://tcfbank.taleo.net/careersection/corporate/jobsearch.ftl?lang=en& In the |Job Number| and |Keywords| fields, we're presenting "Next" as the IMEHint option (tested w/Google and Swiftkey), which prevents user submission of the search. Both Opera and Chrome present the "Go" option for this field.
I think you can use the "Search for Jobs" button below? We usually detect when pressing enter submits a form, and switch to "Go" in that case. However, this page is using JS to submit the form on enter, and we can't detect that. There may be other things we can try though.
Ah, I had filed mainly as a compatibility issue, thinking our code might be missing something. As you point out, there are simple workarounds. Perhaps this is more an evangelism / nice to have enhancement.