The Vālmīki Rāmāyaṇa itself mentions the objective of Indra's visit to Gautama's āśrama which was to simply take away the ascetic powers of Gautama. So, contrary to what the speaker in the video says, in this instance, it was not a test.
After Gautama delivers his curse on Indra, Indra returns to his loka and says:
कुर्वता तपसो विघ्नं गौतमस्य महात्मन: ।
क्रोधमुत्पाद्य हि मया सुरकार्यमिदं कृतम् ।।1.49.2।।
'I have accomplished the objective of the devatas by creating obstacles to Gautama's austerities, evoking in consequence the wrath of the magnanimous sage'.
अफलोऽस्मि कृतस्तेन क्रोधात्सा च निराकृता ।
शापमोक्षेण महता तपोऽस्यापहृतं मया ।।1.49.3।।
'By his (Gautama's) wrath I have been deprived of my testicles. She (Ahalya) has been deserted by him. He has lost his ascetic energy through the pronouncement of this great curse'.
तस्मात्सुरवरास्सर्वे सर्षिस्सङ्घास्सचारणा: ।
सुरसाह्यकरं सर्वे सफलं कर्तुमर्हथ ।।1.49.4।।
'For that reason, O rishis, charanas and great devatas it is your duty to restore my testicles for the benefit I have given you'.
If it is the duty of other devatas to make Indra virile again, it must be the duty of Indra to go disturb the tapasyā of sages. In this instance, however, had Gautama not punished Indra for his despicable act, Indra would have failed his task.
Rāmāyaṇa from Gorakhpur Gita Press also suggests that Indra was just trying to protect his throne:
Deprived of his testicles, Indra with timid eyes then (sought the presence of and spot to the gods headed by Agni (the god of fire), as well as to the Siddhas, Gandharvas and Caranas (as follows):- (1) "Hampering as I did the austerities of the high-souled Gautama by exciting his wrath (and thereby foiling his attempt to claim my throne), I have only just served the cause of gods. (2) In a fit of anger I have (accordingly) been deprived of my virility and Ahalya (too) has been disowned by him. He has (thus) been robbed by me of his spiritual energy by being incited to pronounce a great curse (on me as well as on his wife). (3) Therefore, with (the co-operation of) the host of seers and the celestial bards, O jewels among gods, you should all see me restored to my manhood, since I have served the cause of gods. (4)
The case of Rambhā
Before Rambhā appears on the scene, this is what Vālmīki says:
तस्मिन् सन्तप्यमाने तु विश्वामित्रे महामुनौ ।।1.63.25।।
सम्भ्रमस्सुमहानासीत्सुराणां वासवस्य च ।
महामुनौ when the mighty ascetic, तस्मिन् विश्वामित्रे that Viśvāmitra, सन्तप्यमाने while performing penance, सुराणाम् for devatas, वासवस्य च for Indra also, सुमहान् greatly, संभ्रम: आसीत् perturbance over took.
When the mighty ascetic Viśvāmitra was performing penance, the gods as well as Indra got deeply perturbed.
Again, if Indra's duty is to merely test if a saint has mastered his senses, why should he be a "deeply perturbed"?
So in conclusion, from the sages' point of view, such acts of Indra are for their own good, but from Indra's point, he's just trying to protect his padavī.
OP also mentions:
Indra didn't do any sin in case of Ahalya. Those who have read Valmiki Ramayana verses properly can't deny this fact. Ahalya too didn't commit any sin ...
But the Tilaka commentary says Indra committed a sin:
Why did Indra, the upholder of dharma, engage himself in this sinful act?
He did this mission of the gods, otherwise Gautama would have taken away all the places of gods by means of his severe penance. Gautama rejected Ahalya. This was also the purpose of the gods. When Gautama curses her, his power of penance would be taken away. Had he not cursed, there would have been no loss of penance. In fact, Indra's mission was to arouse anger in Gautama, which would destroy his penance.
PS. One has to simply wonder why Indra and other gods are always trying to protect their posts and also why didn't they make such appearances to disrupt the tapasyā of Rāvaṇa and Kumbhakarṇa.
