There are two similar and slightly overlapping grammar points dealing with the future in the past.
B1 Point 3 in the category of report speech is defined as:
about events in the future with and without backshifts for words relating to time.
B1 point 39 in the category of FUTURE is defined as:
‘WOULD’ future from a point in the past
They said they would call me the next morning with the results.
PELIC STUDENT EXAMPLE:
I remembered that day was Friday and our supermarket would sell a new food ” toasted-duck “, but the manager had no idea how to let customers know how good it was.
A search in iWeb for:
said|told * * following|next _NNT
4 TOLD ME THE NEXT DAY 54
10 SAID THAT THE NEXT TIME 24
11 SAID THAT THE NEXT DAY 22
13 TOLD ME THAT NEXT TIME 19
16 TOLD ME THE NEXT MORNING 16
19 TOLD HER THE NEXT DAY 14