My husband had his card sucked into an ATM when he first moved here. Our bank replaced his ATM card and FedExed it to his office. Since then, we have not had a problem on this side. However, many ATMs have a 2 million IRP limit, so we need to make multiple withdrawals at the end of the month in order to pay staff people. Our bank had to raise our ATM withdrawal limit in order to accommodate this. When our bank saw what they felt were suspicious withdrawals, we get phone calls in the middle of the night. Our bank also seems to limit our withdrawals to three in a day per person, so we sometimes need to dip into our other bank account. I have never had a problem at any of the ATMs that you mention, if you see a logo on the back of your ATM card that matches with the logos on the ATM, it should work. I believe many of them accept ATM cards with the PLUS logo. Another commonly accepted card is the STAR logo.
I just found out that my husband's company has an agreement with Citibank that will cash a check immediately, rather than in 2 weeks, so we can get paid in US dollars and then convert to rupiah. Depending on who your employer is, they may have a similar deal. My husband had worked here since March, and I just found out about this option last week. Anyhow, this avoids any ATM or foreign transaction fees your bank may charge. Our bank does not charge for ATM withdrawals or foreign transaction fees, but they keep telling us we need to switch to an international account, but we still retain our USA residence and have kept a USA forwarding address to get around this problem. I do need to call the bank whenever we return to the states or travel to let them know that the withdrawals will not be fraudulent, they are very good with security and I have never had a problem with any fraudulent transactions, and we have been with them for over 20 years.
During an orientation for my husband's company, I heard that our location is high on the list for fraudulent transactions, especially internet transactions, so your problem might be with your banks security features? If that is the case, call them and explain your situation.