movementpathfinder-2e
Imagine that on each edge of your square stands an enemy, but the diagonals are not occupied (□: unoccupied square, E: enemy, P: player):
□ E □
E P E
□ E □
Do you need to Tumble Through? Based on its text, tumbling is only necessary if you want to be (temporarily) in a square:
[…] During this movement, you can try to move through the space of one enemy.
Is diagonal movement unhindered?
Tumble DC 15:
Tumble at one-half speed as part of normal movement, provoking no attacks of opportunity while doing so. Failure means you provoke attacks of opportunity normally. Check separately for each opponent you move past, in the order in which you pass them (player’s choice of order in case of a tie). Each additional enemy after the first adds +2 to the Tumble DC.
You make a single check as part of your movement if there is only one opponent threatening the squares you're moving through. If two or more enemies threaten those squares, you'll make on check for each enemy (not per square traveled) with a cumulative +2 to the Tumble DC for each enemy after the first.
Example: Your character were cornered by two enemies in a 15 feet corridor with each of them close to the walls and your escape route is behind them and your move speed is 40 feet. You can make a Tumble check DC 15 to move at half your speed and avoid the AoO from the first enemy and another Tumble check DC 17 to avoid the AoO from the second and cross the distance safely with your move action if you succeed in both checks.
Yes, your reading is correct. A medium creature can move through a hostile tiny creature's space, but a small creature cannot (without using optional rules, like tumbling or overrunning [DMG, p. 272]).
In some cases, this makes more sense than others. Keep in mind that small humanoids are about half the size of medium humanoids, and about a quarter their weight (PHB, p. 121), making them roughly the size of a five year old human. Even though these humanoids can be extremely strong, they also are light enough that a relatively small amount of force could reposition them. Certain tiny creatures, like a full grown badger or a hawk (or a Crawling Claw which could carry things twice the weight of an an average halfling), could reasonably impede their movement.
On the other hand, "tiny" is a size category that applies to creatures of quite a variety of sizes. This is a necessity of the rules, since "tiny" is the smallest size category and will apply to anything which is smaller than "small." By way of example a cat, rat, and (normal) spider all all tiny sized creatures, even though these creatures outweigh each other by a factor of 20 (20 spiders to a rat, 20 rats to a cat). As such, a DM might make a ruling in the case of specific tiny creatures that ignores the usual rules on movement (such as deciding that a spider can't impede the movement of a small creature, but a hawk can). However, by the Rules as Written, a small creature cannot move through any tiny enemy creature's space.
Best Answer
It is unclear, but likely yes
Moving through a creature’s space seems to be mostly about how you can avoid ending up in with 2 creatures in one square:
When you move diagonally, there is no chance that you finish in their square, so Tumble Through seems unnecessary.