Someone who is unwilling to come to this free supply of living water to quench their thirst obviously will not be included in the "whosoever".
Someone who is thrilled at the invitation to "come" will respond by coming and receiving this free, living water.
The Greek words used in Revelation can help deal with whether the individual coming is exercising their will in order to drink, or whether an 'outside' will is influencing them. Can the word 'will' be correctly understood as 'shall' - or, what?
In Revelation 17:17 the word 'gnome' is used, a word that means 'mind, judgment, decision'. The context is how the destruction of the vile woman sitting on the beast is suddenly destroyed:
"For God hath put in their hearts to fulfil his will, [literally, to
do the mind of God] and to agree, and give their kingdom unto the
beast, until the words of God shall be fulfilled." Revelation 17:17
K.J.V.
That word 'gnome' is not used in Revelation 22:17. It is 'thelo', which means 'to wish, to will, to mean'. (Young's Exhaustive Concordance used for both text instances.)
In the first text, God influences a desire in the heart of his enemies - to give their kingdom to the beast. Once that desire is roused in their hearts, then they make up their minds to do what their hearts now desire. Thereby, God's will [purpose] is carried out without them knowing their decision actually gets the mind of God carried out by their decision. Until it's too late, of course.
In the text in question, the desire of each individual to get their thirst quenched is already there. It is their heart-felt desire. And so their mind requires no influencing, or changing. Their mind is already in accord with the will of the Spirit and the Bride to accept their invitation. Thus, they willingly come.
Another way of putting this answer is to say that those whose hearts are in accord with the Spirit and the Bride do not need to have an outward influence on making their minds up to come. They will come, because their will is in harmony with the will of the Spirit and the Bride: they come freely, willingly!