Your text was:
Anna sat in her garden and watched the marvelous hummingbirds bout each other for a sip of the nectar. Her attention turned as Paul approached saying, "'Danger is here, follow me, Anna."
Think of your last sentence this way:
Her attention turned(1) as Paul approached(2) (and was) saying(3) ...
1 = the past simple (turned)
2 = the past simple (approached)
3 = the past progressive -- also known as 'the past continuous' (was saying)
Participles are used in various ways. Here is an example in which a present participle is used as a gerund (noun) and so there is nothing even remotely similar to a "tense" connected with the word 'seeing'. The sentence is simply in the past tense -- as determined by the only verb in the sentence, which is 'frightened':
Seeing a ghost frightened him badly.
In the next sentence, a present participle is used, but the meaning is past. The past meaning is determined by the context (in this case, the word 'barged'):
Ignoring the "Do not disturb" sign, he barged into the room.
The sentence above means 'He ignored the sign and barged into the room.'
I can easily add a further present participle to the same sentence:
Ignoring the "Do not disturb" sign hanging on the doorknob, he barged into the room.
In this sentence, some words have been elided: "... sign that was hanging on the doorknob..." So, in this sentence, 'hanging' means 'was hanging'.
Does that help?