As far as I know the Jisho app just shows the same contents as the site. And when I search for sondai on it, I see self-important. Are you sure you're looking at the app associated with jisho.org? There are surely many apps called Jisho in one regard or another, seeing as it's just the word for dictionary in Japanese.
In any case, what you see here on the website is correct. I can't find anything with the meaning of "self-sufficient" on the website or the app.
Jisho.org does not have an app, it's only a website. Look at: https://jisho.org/faq
While there are some suggestions for apps from other people that use the same data sources, that doesn't mean that these apps are kept up-to-date in the same way that Jisho.org is. If you look at the source database you will find the answer to your question very quickly: http://www.edrdg.org/jmdictdb/cgi-bin/entr.py?svc=jmdict&sid=&e=1978364
In May 2018 the entry for 尊大 was modified so that the gloss "self-sufficiency" was removed and "self-important" was added (and some other change). If you use an app that shows the old gloss, well then you know it hasn't kept up with changes in the source database for at least around 4 years. If that bothers you, get a better app ;)
@jakobd2 There might not be one made by the creator of the website, but there is at least one app that does use the Jisho.org API and matches the data, as far as I can tell.
App and website difference
The app for sondai says self sufficient and the website says self important. Which one is correct in the meaning of sondai?