Let's say Newfoundland votes in 1948 to restore responsible government int he first and only referendum vote, meaning it is an independent dominion, rather joining Canada. For whatever reason, the votes are greater in this timeline. Soon after, Newfoundland decides to enter into a customs union with the United States, which the US agrees to. The hope is that direct involvement with the greater US economy will allow the Dominion of Newfoundland to avoid the issues that caused it to be ruled by London in 1934.
This status lasts about a decade, and Newfoundlanders see more and more benefits in becoming a state so that it can directly affect US policy. The customs union has caused a boom in the Newfoundland economy, and more people believe statehood would confer even more benefits. Plus the presence of American bases (a legacy of WWII and now the Cold War) along with American investment sees more natives and Americans comingle and marry.
After Hawaii and Alaska become states, the political climate in the US becomes amenable to the issue due to a patriotic high. After much debate and negotiation, Newfoundland and the US sign a treaty in the early 1960s that sees Newfoundland enter as a state in the union.
The next two decades causes strain due to the Vietnam War and American racial problems. Many Newfoundlanders question whether it was a good idea. But by the 1980s, things have settled down and a new generation has been raised only knowing American citizenship. Proud of their previous status as an independent dominion, Newfoundlanders have a reputation of being something like Texas but more in tune with northern culture.
Because of its status as a state, Americans get use to the idea of 6 major time zones (Pacific, Mountain, Central, Eastern, Atlantic (for Labrador and Puerto Rico, and Newfoundland) for the continental US - ignoring Alaska and Hawaii like normal.