The first "o" in "operator" is pronounced with the "short o" sound found in the word "lot" (typically transcribed in the IPA as /ɑ/ in American English, and /ɒ/ in Southern British English.)
It is indeed the case that a single vowel letter tends to be pronounced as a "short vowel" before a double consonant.
But the inverse is not true: it is not uncommon for a single vowel letter to be pronounced as a "short vowel" when it does not precede a double consonant. Actually, there isn't any one rule that tells you how to pronounce a single vowel letter that comes before a single consonant letter and another vowel letter. Before certain common vowel-initial suffixes (such as -ing, -ed, -er, -est and -y) a stressed vowel tends to be "long" before a single consonant letter (note that words like fading, closest, biker, stony have as their bases words that end in "silent e": fade, close, bike, stone) but there are a number of endings that show the reverse pattern (e.g. verbs ending in -ish, such as famish, perish, vanish, finish, or adjectives ending in -id, such as livid, placid, intrepid) as well as miscellaneous words that just happen to have a short vowel before a single consonant, like camel (in contrast to e.g. label).
In operator, what's relevant is that there are more than two syllables after the stressed syllable. In this context, all single vowel letters except for "u" tend to be pronounced as "short" vowels. This tendency has been given various names, e.g. "Luick's law". It can be seen as related to the phenomenon of "three-syllable shortening" or "trisyllabic laxing", but there are different theoretical analyses that deal with the details in different ways (e.g. "trisyllabic laxing" is often specifically used to refer to a rule about the pronunciation of derived words, and while "operator" is etymologically derived from Latin opus, operis, it seems very doubtful that it should be analyzed as being synchronically derived from the English word "opus").