Look at the code points. It should be:
julia> 'ϕ' # \phi — "straight" form
'ϕ': Unicode U+03D5 (category Ll: Letter, lowercase)
julia> 'φ' # \varphi — "loopy" form
'φ': Unicode U+03C6 (category Ll: Letter, lowercase)
If you get these codepoints with the wrong symbols, then it is probably a font issue. Try switching to e.g. JuliaMono.
Apparently there is some confusion here because the standard glyphs for these two Unicode codepoints were swapped in Unicode 3.0 (in 1999) and some online sources still display them incorrectly, but the standard now clearly states that U+03C6 should now be the “loopy” form if the font is intended to support technical usage:
Fonts used primarily for Greek text may use either glyph form for U+03C6, but fonts that also intend to support technical use of the Greek letters should use the loopy form to ensure appropriate contrast with the straight form used for U+03D5.