Your sentences are both correct but have slightly different meanings. 1. They said there's a hot spring = They said it in the past, but the hot spring exists today. 2. They said there was a hot spring = They said it in the past, and the hot spring existed in the past or maybe it's still there. We don't know exactly. So no, it doesn't always have to be in the past simple tense after "said." Another example is, "They said we were running." "I said that you would go home." "He said we're terrible people!"

You can use it with some other verb tenses. They said they were swimming - past continuous. (a continuous action at a specific time in the past) For example: They said they were swimming in the springs when it started to rain. Or They said they were swimming in the spring at 10 o'clock. They said there had been a hot spring - past perfect (2 actions, one completed before the other.) For example: They said there had been a hot spring there when they were kids. It must have dried up. They said they had been swimming in the hot spring- past perfect continuous (2 actions: a continuous action followed by a second action Or result of a past action,). For example: They said they had been swimming in the hot spring for 20 minutes when it started to rain. They said they had been swimming in the hot spring so they were wet. They said there would be hot springs in- future in the past For example: They said there would be a hot spring, but we can't find it.

Hi, ICECE! "Said" does not necessarily have to be followed by simple past tense. Sometimes, it can also be followed by conditional past. For instance: "She said we should at least think about it." "He said there would be cake at this party." "My mother said I could play at the park." It can also be followed by past perfect tense: "My friend said he had already swum ten laps today." Regardless, "said" should be followed by some form of past tense, since "said" is the past tense form of the verb "to say." The only time it isn't is if we're quoting someone directly. For instance: "My teacher said, and I quote, 'It is essential that you pass this upcoming test, because your entire career depends on it!'" I hope I've helped answer your question. Please let me know if I haven't.

It is said that there is a hot spring.