Goldfish and tiger fish have no business sharing an aquarium. These two species come from different environments and require vastly different aquarium conditions to thrive. On top of this, behavioral issues make them even more incompatible. Keeping these fish together can only end in disaster.
The first barrier to keeping these fish together is their temperature requirements. Goldfish come from temperate conditions, so they do their best in water between 68 and 72 degrees Fahrenheit. But all species of tiger fish come from tropical climes and need water of at least 75 degrees. This does not mean that water warm enough for tiger fish will kill goldfish, or water cool enough for goldfish will make tiger fish instantly go belly-up. But keeping a fish outside of its ideal temperature range stresses fish and leaves it more vulnerable to disease.
Since goldfish and tiger fish come from different environments, they have adapted to different suites of pathogens. This means that goldfish are resistant to germs that can harm tiger fish, and vice versa. So when you keep these species in the same aquarium, one tends to give others diseases to which they have no resistance.
Goldfish and tiger fish both require a lot of room. While this does not preclude them from sharing a fish tank -- though other things do -- it does further complicate maters. Tiger fish need at least 65 gallons of aquarium volume per fish, and some species of tiger fish prefer to live in groups. Meanwhile, goldfish need at least 30 gallons of aquarium volume per fish to truly thrive. Goldfish kept in smaller tanks tend to get stunted growth and live shorter lives. A healthy goldfish can live more than 40 years and grow longer than 8 inches. So you would need a huge tank to accommodate both goldfish and tiger fish -- and even then there are other reasons to keep them apart.
Several species have the common name "tiger fish." All are predatory to various degrees, making them poor companions for goldfish. The African tiger fish (Hydrocynus vittatus) will take bites out of fish larger than itself. Others, like the silver tiger fish (Datnioides polota) and Indonesian tiger fish (D. microlepis) will generally not bother fish the same size as themselves. However, these fish rapidly grow to about a foot long, and many goldfish are sold at smaller sizes, making them bite-size treats for tiger fish before they reach maturity.