To me? Absence should be two syllables as in ab-səns.
M-W.com has two syllables: [ab·sence]
But dictionary.com has three syllables: [ab-suh ns]. I can understand that giving certain accents and regional pronunciations.
Syllable counter has "by their absence" at three syllables (the starting bit of confusion for me that sent me on this minor word journey). Really doesn't make any sense. How would one say that word in one syllable? Never had a problem with this site before. Seems like a very existential glitch.
If you need to consult a dictionary to count syllables for haiku next time you visit dictionary.com to look up
absence
[ab-suh ns]
note that the expression in square brackets to which you refer provides a guide to pronunciation.
Underneath that line is a box labelled Syllables
When you click on that tab the word "absence" is shown split into its syllables viz. ab·sence
Then you count the number of syllables that the word has been divided into.
I did exactly that (all that is stated in the OP). That's where the problem lies. Different dictionaries are providing different answers. Ultimately, I went with the answer that allowed me to write the line I wanted to use.