Every class file has options that set the font size; the
\ExecuteOptions
command sets the defaults. In your case, that line is
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This implies 10 points. Their advice to use
mathptmx (I prefer
txfonts, which uses the same body font but does some math symbols differently and does other things as well) suggests they want Times size 10pt.
Most journals are OK with Times or Helvetica (or clones thereof) for images. Using EPS format might even allow them to change your fonts, if necessary, to match the journal's preferences (I have encountered a publisher who did that).