The timezone widget does not reliably trigger. In my experience, it is only activated when two specific timezones are entered (e.g. EST and GMT), not accepting countries/regions in their place. It also does not recognise some timezone abbreviations, like SGT. See screen recordings below with examples, compared to Google.
Kagi
Google
As a side-note, I also feel that the conversion widget's UI could be updated slightly to reflect the rest of Kagi's sleeker look.