"Why it is believed that it will give positive effects only if it is Lord Shiva's own wish to perform Tandava and not of others?"
I'm not sure from where do you get this idea. But in Narada Purana we see Sage Jaimini asks to do Tandava for Shiva and Lord Shiva happily does it and result is also described auspicious:
Here is relevant part from Narada Purana II.73:
Jaimini said : "O! God of gods, the Lord of the universe, I am blessed, I feel that I have accomplished all objectives of life in as much as you who are worthy of being meditated upon by great gods like Brahma and others have personally revealed yourself before my eyes.”
Then the delighted lord Girisha placed his hand on Jaimini’s head and told him—“O dear son, tell me what you wish ?
On hearing those words of Sambhu, Jaimini replied, “May I see the lord accompanied by Amba, Vighnesa and Kumara."
Then Sankara appeared before him accompanied by his son as well as by Amba.
Then the delighted lord asked again—“Tell me, dear son, what do you wish ?"
On seeing the merciful nature of the lord, of the preceptor of the universe, Jaimini smilingly said—"May I see you performing the Tandava dance."
Then, in order to fulfil that desire of his, lord Ambikapati remembered Siva Pramathas who are experts in different sports.
The moment they were remembered, all of them led by Nandin, Bhringi and others came there chattering enthu-siastically. After bowing down to the lord accompanied by Vighnesa, Kumara, and Amba they remained silent and stood there with palms joined in reverence. They eagerly waited for the behests of the lord of the Devas.
Then at the behest of Jaimini, Shiva assumed a wonderfuul form with ornaments and dress of variegated nature, and began to dance. He shone with the tremulous creeper like serpents appearing as kindled fire. A slight smile flickered over his face. The crescent moon rendered the forehead splendid. His arms were lifted up like a banner. ...... ........ .......... ........... ... The devotees who were highly delighted shouted cries of victory for him. The lord shone brilliantly with the Tandava dance that followed. He brightened the quarters.
Then, on seeing the dance of Mahesa Jaimini was immersed in the ocean of bliss. With great concentration, he eulogised the lord with hymn consisting of verses having one quatrain from the Vedic texts in each. ...... ...... .......... ........ ...... After eulogising Siva thus with this hymn, that great sage, bowed down to Sabhapati. His eyes were filled with tears of affection.
He frequently imbibed the auspicious nectar of the Tandava of Isha. After attaining all cherished desires, he obtained the state of being the Ganapati.