Repeat by:
This resulted in wikitext:
foo{{Citation needed|date=December 2018|reason=this -> that}}which rendered as:
<span title="this -"> that (December 2018)">citation needed</span>
PS:
Chrome Version 70.0.3538.110 (Official Build) (64-bit)
MacOS 10.13.6 (17G3025)
https://en.wikipedia.org/w/index.php?title=User:RoySmith/sandbox&oldid=873327421
Thanks for the bug report!
I think this is the expected behavior – unfortunately, when you edit a template inside VisualEditor, the template parameters are only editable as wikitext and not visually :( (see T52355). So whatever you type in the template dialog, will be included exactly as-is in the output wikitext.
By typing this -> that into the "Reason" field, you end up with |reason=this -> that in the output wikitext.
The messed up rendering of that wikitext is weird, but it's not a problem with VisualEditor. The same problem appears for the wikitext <span title="this -> that">citation needed</span> (without using the template). The behavior of the wikitext parser here is definitely questionable. I filed a separate task about this problem: T211816: Wikitext parsing of unescaped < and > inside tag attributes is unexpected (different from HTML rules).
I guess you need to manually replace the > with >. (Also, perhaps the "Citation needed" template on English Wikipedia could be made to magically apply this replacement automatically? Try asking on the discussion page there.)