You did that only for a single character SHIN?  But the image shows
that the entire string is displayed by a font that is not DejaVu Sans
Mono.  And at least on my system, DejaVu Sans Mono doesn't have glyphs
for the Hebrew block, so when I tell Emacs to use DejaVu Sans Mono as
the default font, the Hebrew letters are displayed using a different
font.

If you don't apply the text property, do you see the Hebrew text
displayed by DejaVu Sans Mono, or does Emacs use a different font for
it?  And what does describe-char say about that if you don't apply the
text property?

> Apparently, this is what is causing the issue.

It could be, but I don't see how this could happen, by just looking at
the code involved in this.  I'm probably missing something.
It is "emacs -Q". My default font is DejaVuSans Mono. Hence H is displayed using the same. The Hebrew text is using Linux Libertine Display O. For printing, I needed text with font variation. So I applied the text property for weight and slant - though it didn't change the appearance. After that, desc-char starts reporting as mentioned in OP.