At this age, he also may need to be wormed, even if he has had one dosage, some parasites require a second dose to effectively kill all worms.
I would not consider whiskas a premium food, you might try Royal Canin, Nutro, even Iams kitten would be suitable.
I prefer to feed Hills A/D canned to my younger kittens with either warm water or KMR to make it more of a mush, and around 6 weeks begin crushing dry kibble into the food to slowly wean onto kibble. Hills A/D is very easy to digest for young kittens and seems to be very palatable as well.
What color is the stool, yes it does sound to be diarrhea. The stool color could also indicate a bacteria imbalance, so feeding a little plain yougurt would help to get to replenish the good bacteria.
He could just be stressed with all the new surroundings, which could be bringing on a bout of loose stool.
Dehydration is the biggest concern with diarrhea. Make sure your kitten continues getting plenty of water. A kitten this age can become dehydrated in as little as 6 hours.
If the kitten does start showing symptoms of dehydration, you can syringe a few cc's or ml's of Pedialyte with 50% water dilution to help restore the kitten.
You can also give childrens Immodium A/D. I would assume this kitten is around 1lb, check weight before hand, but our vet suggests 0.25 cc's or ml's of Childrens Immodium A/D per pound to firm stool.
I would bring a stool sample into the vet as soon as you can, to have a fecal done. Your vet will be able to help give medication if it is needed.
Congratulations on your newest furry family member. How wonderful that you rescued him!!