Neither is correct. The correct way is: com•mu•ni•ca•ting.
Hyphenation is used to break up words at syllable boundaries, so the problem is knowing where the syllable boundaries are. The rule is called the Maximal Onset Principle.
Syllables are made up of three parts: the onset, nucleus and coda. The nucleus is the vowel part, including diphthongs. The onset is consonants before the nucleus, and the coda is consonants after the nucleus. So in the word "scout", "sc" is the onset, "ou" is the nucleus, and "t" is the coda.
The maximal onset principle states that consonants are grouped in onsets as much as possible, rather than codas. In simpler terms, put as many consonants at the start of a syllable as you can, rather than the end of the previous syllable.
In the word "communicating", there's several places where it's not immediately obvious to which syllable the consonants belong, but the maximal onset principle gives one clear answer. For instance, the "n" belongs in the syllable "ni" because it can be part of the onset of the nucleus "i".
This doesn't mean all consonants go to the onset, just the ones that the language allows. Take the word "instruct", for example. Between "i" and "u", there's "nstr". In English, we can't begin a syllable with "nstr", so we look for the longest string of consonants that English does allow in an onset, which is "str". This means "instruct" syllabifies like this: in•struct.
As for the "m•m" part of "communication", there's a writing rule that in English we always separate double consonants, even though the sound belongs only to the syllable after the break.
There are other rules for hyphenating writing that cause computerized hyphenators to make mistakes, including attempting to break words at word boundaries within the word. For instance, in the word "newsletter", the maximal onset principle would break it as "new•sletter", which is obviously wrong because it breaks the word "news". The two algorithms that hyphenated "communicating" in the website you used were possibly trying to preserve the words "at" and "cat".