Question: Situations manifest in our lives as karmaphala, due to our previous deeds. However, many people say that after they put on a gemstone or started worshipping some Demigod, things changed for them.
My Reply: People in general are amazingly ignorant (avidyā) of themselves and their world. We cannot take their testimony very seriously. We take the testimony of siddhas, yogis, sādhus, and ultimately above all we take the apauruṣeya testimony of the Veda. Some people will think that because they sneezed three times in a row just before they got some bad news, then if they ever sneeze three times in a row again it will be catastrophic for them. This is called coincidence, but people in general cannot sort out coincidence because they are very intoxicated (sammoha) by rāga, dvesha and all sorts of emotions and attachments and hopes and fears.
Question: Ok, but Bhagavad Gita also talks of Demigod worship and awarding of results, albeit through Krishna.
Yes, this is called karma. The effort to respect the forces of nature (“demigods”) is a very important part of the effort to do proper behavior (sad-karma) and thereby get good results (sad-karma-phala). Krishna is not involved in this – he merely allows the situation to exist because entities such as us desire it. See Gita 9.9 & 10.