CaptionHub spellchecks in the browser as you type according to the default settings of your browser. This means spellcheck is probably only active for the caption that's selected. If you'd like to run a final spellcheck after you've finished translating, then click on the cog drop-down menu, and select Export text for spellcheck.
This will download a text version of your caption set, which you'll be able to spellcheck in a text editor or word processor.
Once you've finished, you have the option to save the file (in its original format), and re-import back into CaptionHub. In which case, select Import text from spellcheck, and CaptionHub will replace all the subtitles in your captionset with the corrected ones.
Warning: Microsoft Word treats text files in a non-standard way, and CaptionHub is likely to fail a spellcheck round trip. Please use an alternative word processor.