SMP does not post or mention the policy, unless they need to. I repeated the policy from experiences I have had over the past six years.
On three of my Caminos, I arrived significantly earlier than my reservation dates. They permitted me to stay for the duration of my need. In one case, this was a full week. SMP remains my default sought after room on arrival at Santiago. But, in the past couple of years, it has become increasingly unattainable by advance email reservation.
Being able ti get a room for more than a night or two It depends primarily on WHEN you are arriving. For example, if you arrive in April or early May, or in late September or October, before or after the season is in full-swing, you might be able to stay longer.
But from June through early September, it is difficult to find space. That is one reason why ANY accommodation needed at Santiago on arrival, during the summer months, needs to be booked and confirmed in advance.
In particular, in recent years large groups of pilgrims (schools, scouts, churches, civic groups or clubs) have found they can advance reserve blocks of rooms at SMP. Evidently, management is just trying to fill the rooms. Advance group bookings are more reliable for room management that solo pilgrim reservations.
In the summer months, this practice consumes most rooms on most weeks. Also, if the Spanish military is in town for one of their many annual ceremonies at the Cathedral, SMP is literally booked to overflowing.
During the peak summer months, solo pilgrims are used to "fill in the gaps" between the groups, at least in my perception.
While SMP remains the single best housing deal in town for pilgrims, the secret is out and solo pilgrims are usually on the losing end. I expect this condition to get worse as the Holy Year (2021) approaches.
Hope this helps the dialog