Modelling question when having two timestamps in a fact table

I would do as you say and split the table into multiple rows, one for each hour covered. You could do this in SQL, Power Query or DAX. Below is a sample in DAX

SELECTCOLUMNS(
	GENERATE(
		'Table',
		VAR StartYear=  YEAR( 'Table'[Start] )
		VAR StartMonth = MONTH( 'Table'[Start] )
		VAR StartDay = DAY( 'Table'[Start] )
		VAR StartHour = HOUR( 'Table'[Start] )
		VAR StartMinute = MINUTE( 'Table'[Start] )
		VAR NumHours = DATEDIFF( 'Table'[Start], 'Table'[End], HOUR )
		VAR EndMinute = MINUTE( 'Table'[End] )
		VAR Result = SELECTCOLUMNS(
			GENERATESERIES( StartHour, StartHour + NumHours ),
			"Hour number", [Value],
			"Start date", DATE( StartYear, StartMonth, StartDay ),
			"Minutes worked",
			VAR StartOfHour = DATE( StartYear, StartMonth, StartDay ) + TIME( [Value], 0, 0)
			VAR EndOfHour = DATE( StartYear, StartMonth, StartDay ) + TIME( [Value] + 1, 0, 0)
			VAR MinsWorked = DATEDIFF( MAX( StartOfHour, 'Table'[Start] ), MIN( EndOfHour, 'Table'[End] ), MINUTE )
			RETURN MinsWorked
		)
		RETURN Result
	),
	"User", 'Table'[User],
	"Task", 'Table'[Task],
	"Start date", [Start date],
	"Hour number", [Hour number],
	"Minutes worked", [Minutes worked]
)

In this I have stripped out the time part of the start time and left just the date, so that it can be linked to a normal date table.

If you expect the time periods to cross midnight into another day then you will need to implement additional logic to correctly calculate the StartOfHour and EndOfHour variables, but everything else should work the same.