Hi Agua,
As I understand it Saul didn't die the next day but rather 2 or 3 days later.
Morrow means next day as scripture does say the next day as being in to
morrow that the Philistines attacked Israel and wounded Saul and it was the same day of battle that Saul was wounded and killed himself by falling on a sword
1Sa 28:19 Moreover the LORD will also deliver Israel with thee into the hand of the Philistines: and to
morrow shalt thou and thy sons be with me: the LORD also shall deliver the host of Israel into the hand of the Philistines.
1Sa 31:1 Now the Philistines fought against Israel: and the men of Israel fled from before the Philistines, and fell down slain in mount Gilboa.
1Sa 31:2 And the Philistines followed hard upon Saul and upon his sons; and the Philistines slew Jonathan, and Abinadab, and Malchishua, Saul's sons.
1Sa 31:3 And the battle went sore against Saul, and the archers hit him; and he was sore wounded of the archers.
1Sa 31:4 Then said Saul unto his armourbearer, Draw thy sword, and thrust me through therewith; lest these uncircumcised come and thrust me through, and abuse me. But his armourbearer would not; for he was sore afraid. Therefore Saul took a sword, and fell upon it.
1Sa 31:5 And when his armourbearer saw that Saul was dead, he fell likewise upon his sword, and died with him.
1Sa 31:6 So Saul died, and his three sons, and his armourbearer, and all his men, that same day together.