Short answer:
You can't think of "the other territories" as one experience-- these were vastly different places, with very different kinds of economies, enormous differences in scale and history; the response to the Depression has to be considered in each case separately.
The Philippines were by far the largest of these territories, had a complex economy and a diverse response. Hawaii and Puerto Rico both had substantial populations-- the Depression conditions were likely worse in Puerto Rico; major hurricane damage, less military spending than in Hawaii, but also a more ambitious New Deal policy response. Alaska, Guam and USVI had tiny populations, Alaska in particular would have been largely unaffected with little integration into the world economy
Discussion:
Alaska's population in 1930 was 59,000; was still substantially Inuit and hunter/trapper/settlers, living traditionally or near traditionally, with little to no integration into the world economy. A recession or depression doesn't matter much to people hunting for their food, making their own clothing, living "off the grid". Fur trappers and traders presumably experienced a decline in cash (or barter) earnings, but I can't find any documentation for that. The Klondike and Alaska Gold Rush was long over by the 1930s, fortune hunters had dispersed, you'll see population declines in some years of the teens and twenties.
Hawaii was far larger -- 360,000 in 1930, and much more integrated into the economy. In this period, sugar was the engine of the Hawaiian economy, and the Depression hit sugar (and also pineapple) exports hard; something like one quarter of the workforce was counted as unemployed by 1935. Military preparations following Japan's occupation of Manchuria brought a great deal of investment, along with military personnel spending money to Hawaii by the late 1930s.
The Philippines, by far the most populous of the places you mention (population near 13 million in 1930) had considerable export exposure, but seem to have done reasonably well during the Depression, with a diverse economy not subject to any one shock:
There is no doubt that the early and mid-1930s were not normal or generally prosperous times in Manila, but the city's economic complexity was such that there were offsetting conditions that mitigated the impact of the depression in most years. When exports were down in 1931 and 1932, employment in construction was up. When construction was at a low level in 1934, exports were up. When these were off together in 1935, female employment in cigarmaking was up, and the coconut oil mills were near peak production.
Guam was tiny, 18,000 people in 1930. During the 1930s, Guam became an important communications node with a seaplane base, transpacific telegraph station, and a Chamorro population living traditionally or near-traditionally, substantially unaffected by the Depression. Of documented effects, you see the failure of the newspaper, the Guam Recorder, which is then bought by the US Navy. The Navy's influence was the dominant force in the cash economy of the island in the 1930s-- there was little integration into a secular global economy.
Puerto Rico had a relatively large population of 1.5 million in the 1930 census, and an economy which beyond subsistence farming was dominated by sugar. The situation was made much more difficult by a devastating hurricane San Felipe which hit in 1928; the challenges of the Depression piled on an already difficult situation. The situation remained difficult throughout the 1930s, leading to considerable political and social discontent. Roosevelt's New Deal included a The Puerto Rico Reconstruction Administration, which pursued the "Plan Chardon" -- one of the only genuine land reform initiatives in US history, this involved the purchase of large sugar plantations in excess of 500 acres, though it was never fully implemented. Other projects included public health and housing.
Virgin Islands
Again, a tiny population in 1930 -- 22,000 people. I can't find any scholarly resources on their experience in the Depression, but as a sugar exporter the decline in international markets would have been felt. The USVI were a very new bit of the United States in the 1930s-- purchased from Denmark in 1917 for $25 million, they were administered by the Department of the Navy until 1931, then transferred to the Department of the Interior which appointed civilian governors. There was little to no tourism before the Second World War. The first Naval Governor regarded conditions as very poor before the Depression
. . [T]he urgency of the overwhelming clean-up task that the Americans were forced to undertake immediately upon assuming control of the islands in 1917. Naval administration Governor James Oliver presented the grim reality in his first annual report to the secretary of the navy, writing that "the problems to be faced in the most elementary improvement of the present conditions in these islands with particular reference to sanitation, hygiene, public morality, finances, etc., are so many and so grave." Hospitals, health, and sewage systems were in unspeakable condition. There was no water system, a minimal and ineffective education system, no fire protection, and, worst of all, no employment for the population.
Sources:
Metropolitan Manila in the Great Depression: Crisis for Whom?
THE CRISIS OF THE 1930S in Enciclopedia de Puerto Rico
Economic History of Puerto Rico
1930 Federal Population Census
A Question of Custody: The Colonial Archives of the United States Virgin Islands
There's relatively little published material for most of these subjects-- Puerto Rico has had the most scholarly interest, then Hawaii-- the National Archives have more material, like reports of the Governors, but this is all offline so far as I'm aware.