Yes. On my end everything seems to work.
This is definitely not an issue with the plugin (and very likely not an issue with the theme either), it is not possible for the same code to execute with the same parameters and have different outputs.
The same pageview is giving different outputs, and that is not possible – unless there something in the middle, which changes the output at will – like a cache plugin, CDN or something on the server side – check opcode cache, other type of opcache, memcached and similar modules.
I could only replicate this one time – on the first pageview the old search was there, on the second (and every pageview afterwards) the new search. Even when I edited the theme code to not show anything, it had no effect – so some sort of a cache on the server side is present.