Aorist Tense:

Simple fact.
Once and for all.
Specific.
 

1st Aorist Tense Forms: Participles

ἡ δὲ Μέλιττα οὕτω μακρὰν τῇ προτεραίᾳ  βαδίσασα ὑπέρκοπος ἦν.
And Melitta, having done so much walking the day before, was worn out.
The meaning here is: because she had walked so far the day before.... .
You have to remember that the aorist always means: simple fact, specific action and does not necessarily refer to the past, except in the indicative (stating past facts).
The action expressed by the aorist participle does however usually take place first, the other action, whether in the past, the present or the future is the last in any sequence:
ἡγησάμενος αὐτοῖς εἰς τὴν αὐλὴν τῷ βωμῷ προσεχώρησε
καὶ σπονδὴν ποιησάμενος τὸν Δία ηὔξατο σῴζειν πάντας ....

Having lead them into the court-yard he went to the altar and
having made a libation he prayed Zeus to keep them all safe.

That's what the participle-loving Greeks said, we would say: He lead them into the yard, went to the altar, made a libation and prayed Zeus to keep them all safe.
A series of simple, specific actions that took place/happened some time in the past.
And if we want to tell someone that these actions always take place before a journey?
We just have to change the aorist indicative (past) to present indicative.
And the participles?
We have to leave them in the aorist, because they refer to actions prior to "approaching the altar" and prior to "praying Zeus":
ἡγησάμενος αὐτοῖς εἰς τὴν αὐλὴν τῷ βωμῷ προσχωρεῖ καὶ
σπονδὴν ποιησάμενος τὸν Δία εὔχεται σῴζειν πάντας ....
And if we want to tell someone that these actions will take place tomorrow?
We just have to change the aorist indicative (past) to future indicative.
And the participles?
We have to leave them in the aorist, because they refer to actions prior to some other action in the future.
ἡγησάμενος αὐτοῖς εἰς τὴν αὐλὴν τῷ βωμῷ προσχωρήσει καὶ
σπονδὴν ποιησάμενος τὸν Δία εὔξεται σῴζειν πάντας ....
 If of course  we want to say that Dikaiopolis prayed/prays/will pray to Zeus while (=at the same time as) offering a libation, then we must use the present participle ποιῶν instead of ποιησάμενος for simultaneousness of actions (past, present or future)

Further examples from the text:

τὴν Μέλιτταν χαίρειν κελεύσαντες ὥρμησαν.
ἡ δὲ μήτηρ βοήσασα, 'ᾦ τλήμων παῖ,' ἐ̓́φη
οἱ παῖδες, τὴν θεὸν θεασάμενοι, ἐκ τοῦ ἱεροῦ ἐξῆλθον.

 
active participle        middle participle
      NO past tense marker                 NO past tense marker 
  βαδίσ    2nd aorist stem    ποιησ    2nd aorist stem 
     ας 
     ασα 
     αν 
  active participle marker (m)  
  active participle marker (f)
  active participle marker (n)
     άμενος 
     αμένη 
     άμενον 
  middle participle marker (m)  
  middle participle marker (f)
  middle participle marker (n)