This statement I think can be agreed with in part when it is applied to the text of "Ulysses." This is because the poem does definitely capture the spirit of exploration and adventure that characterised the Victorian age, which was one of massive colonial expansion. Note, for example, the way in which Ulysses expresses his desire for continual adventure:
Come, my friends,
'Tis not too late to seek a newer world.
Push off, and sitting well in order smite
The sounding furrows; for my purpose holds
To sail beyond the sunset, and the baths
Of all the western stars, until I die.
Tennyson himself had lived through various "newer worlds" that had been, if not discovered, at least colonised by Britain, and therefore this poem can be said to relate to the "aspirations and vaulting ambitions" of Victorian times.
However, at the same time, there are aspects of this poem that are definitely not part of Victorian beliefs and society, and these concern the way in which Ulysses could be viewed in a much more negative light. Far from being a figure who is viewed as an adventure-seeker and who is brave and courageous, it is possible to view him as a character who does not do his job, and leaves behind his kingdom of Ithaca, and its people, in a somewhat irresponsible way. Not only this, but he is very dismissive of his subjects, that he describes as if they are almost animals. They "hoard, and sleep, and feed, and know not me" and are a "savage race." If the Victorian period of history focused on colonial expansion, it also very strongly focused on consolidation, and this is something that is not expressed in this poem that courts adventure at the expense of loyalty and responsibility.