Tonga was a protectorate of the British Empire from the "Treaty of Friendship" in 1900 until Tonga withdrew in 1970 and joined the British Dominion instead.

So it really depends on how you want to look at it. The Monarchy in Tonga was not abrogated, the local courts and institutions were not replaced or reformed along British lines (except by the choice of Tonga elites). Queen Salote Tupou III's rule (1918-65) is considered a high point in Tonga politics and culture because of investments she made in the arts, history, genealogies, and archeology. She was part of the Tongan State's own assertion of identity and there was never any question whether or not she was acting independently or as a monarch ruling in the name of the British Monarchy. She is not considered to have been subordinate to the British crown.

So it terms of colonialism being an unequal power relationship in which culture and political power are reordered and subordinated to a colonial state-- well that never happened. Tonga experienced nothing like the massive land alienations of Hawaii, New Zealand, or New Caledonia. It never had large outside labour populations brought in as Fiji or Australia. It never had a forced political reordering like Samoa or a forced division like that of Samoa/American Samoa.

The likely reason why Tonga is colored in on the map is the Treaty of Friendship in which Britain became the 'protector' of Tonga and Tonga granted to Britain the right to represent it diplomatically in all foreign affairs. So did Tonga surrender sovereignty to the British or did they maintain sovereignty but surrender some sovereign powers? I would say the second category is probably a better characterization of the relationship. After all, if Tonga had surrendered total sovereignty to the British Empire, then it's odd that they would have the right to unilaterally end (or change) that relationship.

Effectively, the Treaty of Friendship made Tonga an autonomous protected Kingdom within the British Empire, thereby protecting Tonga from advances by either the Germans or Americans who had all too recently carved up neighboring Samoa in 1899.

Tonga officially maintains the point of view that it was never colonized, because this relationship was voluntary, because it could be unilaterally ended, and because the monarchy never lost domestic control. That is the official history-- an unbroken modern united Tonga from 1844 to present with a much longer/deeper time history of empire as well. I don't think this version of history is wrong though there is clearly a political and cultural reason for presenting the history of the state as long and unbroken. Certainly Tonga avoided the sort of traumatic colonialism of its neighbors and so I think it is fair to say it was not colonized despite agreeing to assign Britain some sovereign powers.