The established view on massive IoT access is that the IoT devices are activated randomly and independently. This is a basic premise also in the recent information-theoretic treatment of massive access by Polyanskiy. In a number of practical scenarios, the information from IoT devices in a given geographical area is inherently correlated due to a commonly observed physical phenomenon. We introduce a model for massive access that accounts for correlation both in device activation and in the message content. To this end, we introduce common alarm messages for all devices. A physical phenomenon can trigger an alarm causing a subset of devices to transmit the same message at the same time. We develop a new error probability model that includes false positive errors, resulting from decoding a non-transmitted codeword. The results show that the correlation allows for high reliability at the expense of spectral efficiency. This reflects the intuitive trade-off: an access from a massive number can be ultra-reliable only if the information across the devices is correlated.