Then I might get it.
We have our own Chinatown , a Koreatown and a few Japanese Supermarkets, I *have* bought a Chinese Hot Chili Sauce, very smooth and creamy, think "red condensed milk" in texture, and not long ago saw a chili+garlic one, probably very close to what you mention.
Not available in flexible tubes, but in 1 kilo / 2 pound glass jars, think marmalade type.
Probably not many Family type users, so they straight import the larger Restaurant sizes.
On Tuesday it's my Birthday, might very well invite close Family to some Chinatown Restaurant and check for the sauce.
Anyway I go there regularly to buy chinese rice flour pasta and fresh Tofu, Melona ice cream and that weird chewing gum flavoured soda..