The built-in spellchecker functionality of the editor is activated only after you press the AJAX spellchecker
tool. After that the misspelled words are highlighted with yellow background (if not modified) and not with red squiggles.
I suppose the mentioned squiggles comes from the browser's spell checking feature. I am attaching two snapshots, one with the browser's spell check highlighting and one with the editor's. Please compare them and get back to me if I am somehow mislead to the origin of your problem.
If the problematic case is the browser's feature there is no way to manage its library programmatically from the editor's API, because the functionality is implemented inside the browser's core.
Nevertheless, you could check these articles about how to manage or disable this feature in:
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