Strict sequence-of-tenses gets muddy when Speech time, Event time and Reference time overlap, as in your instance.
When I got home yesterday, John called and said he will arrive next week.
Here, the Event time (next week, the time of the event ‘I’ am speaking about in this clause) happens to lie in the future with respect to both the time when John called (yesterday) and the time in which the sentence is uttered (Speech time). Consequently, ‘I’ may use either as the Reference time (the point in time to which the event is related) for speaking about that event:
John called yesterday and said he would arrive next week. ... Here Reference time = the time of John's call.
John called yesterday and said he will arrive next week. ... Here Reference time = Speech time.
Note that there are opposed pressures here. On the one hand, the time of John's arrival (the Event we are concerned with) was pinned down in his call, so there's pressure to use the time of the call as the Reference time and use would. On the other hand, the phrase next week takes Speech time as its Reference time, so there is some degree of pressure for the event which it modifies to do the same and use will. The two pressures balance, and you may choose whichever is more appropriate to what you are trying to communicate:
I'm so excited! John said he will come next week!
John said yesterday that he would arrive next week, but I think he underestimated how long it would take him.
You are only required to use would if Event time lies in the past with respect to Speech time and you are relating Event time to a time even farther in the past:
John called on the 15th and said then that he would arrive on the 20th; but it's now the 30th and he still isn't here.
Here the Speech time is the 30th; the Event time for John's arrival is the 20th; and it is related to a Reference time of the 15th.