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From what I know, if we are talking about a rule, zero conditional should be used. Therefore, proverbs using "if" should use zero conditional (http://www.1-language.com/englishcoursenew/unit40_grammar_exs.htm).
However, I've come across some proverbs that use the first conditional:
Choose a job you love, and you will never have to work a day in your life.
If you play with fire, you’ll get burned.
Any idea why?
Your linked article contains this statement:
"The zero conditional (using If you can't...) is often found in old sayings and proverbs."
This is true, it often is, but that doesn't mean it always is. Proverbs are defined as "stating a general truth or piece of advice". Advice isn't the same as an inescapable fact, which a zero conditional statement usually conveys, so don't expect all proverbs to follow that format.
Regarding your specific example - although conditional statements tend to use "if" or "when", there are lots of other ways of phrasing such a statement either omitting or replacing "if". For example:
These all mean the same thing - that if condition [x] is true, it follows that [y] is true.
