Just wondering, but was this the first time this XT had been turned on for a while? From what I have read about this, tantalums are generally extremely reliable and do not degrade with time the way that standard aluminum electrolytics do. If they fail it is usually from long term storage (20+ years) or poor storage conditions, then being powered up once they have shorted internally. The really obvious and scary way they fail has made them notorious, not necessarily that they have a really high failure rate.
I have only experienced two tantalum failures in all my years of computing. One was a Trident TVGA8900B that popped and smoked about two years ago when I first powered it up, the other was a brand new in box Everex EGA+Parallel card that I got about 3 years ago... that one simply had a shorted tantalum (no explosion or smoke) that I replaced with a random old aluminum electrolytic with the same rating (it was all I had at the time and that card has worked perfectly since the repair). In both situations the cards hadn't been used in decades (the everex card was over 30 years old and had never been powered up) the Trident was a slow ISA card from ~1990 so it's doubtful it was used in the last 25 years.
One day last summer I photographed every single card I had with SMD or through-hole tantalums and cataloged the ratings of their caps in case any ever blew up (they are usually unrecognizable when they go, making it hard to know what to replace them with). I then took ALL of these cards, ISA, PCI, AGP and VLB, outside with some motherboards and power supplies. I covered the setup with a plastic tote to shield myself from the explosions. I took several hours testing cards... probably between 50 and 75 cards from the mid 80s 8bit PC\XT era to late 90's AGP cards with SMD tantalums. I'd swap a card, cover it up, power on the system and wait a few minutes with it running. The result? Not a single failure.
Since then I've tested many more cards, some very odd, very old and very unlikely to have been used in the last 20 years, and I haven't had another explosion or even a shorted cap.
Replacing every tantalum on vintage boards is excessive and unnecessary in my opinion. There are tons of tiny tantalum capacitors in cell phones and other modern electronics. If they were actually THAT bad, they wouldn't still be in use. That said, tantalums are expensive so unless you're a stickler for keeping things looking original, replacing them with a low ESR electrolytic or some other modern capacitor that didn't exist 30 years ago is probably fine. I am not an engineer or all that knowledgeable about the details of these things, I can only tell about my (limited) experience, for what it's worth.
Now for some blitting from the back buffer.