More than a bit late to this but perhaps you have enabled or disabled search_fragment which does change slightly how search operates. Check the page to see exactly which configuration is more helpful for your use case.
Other than that, notice that DW does need ASCII quotes for phrase search (which is also affected by the above setting). ASCII ("straight") quotes are a universal phrase delimiter in most programming languages and language contexts, as they do not depend on the local language of the user / wiki, wheras other punctuations are defined per-country, per-language or per-locale (for example, Spanish has curly quotes, and IIRC French has quote-below and quote-above; furthermore other languages might use completely different symbols at all).
On mobile, the only thing I can guess would help with this regardless of your chosen keyboard software is to disable autocorrect options that change text that you've already written, such as typographical replacements ("" to “”, parens to smileys, or blending punctuation into arrows like DW does). But my experience with mobile is fairly limited, so there's likely better ways.