system
Given the following post, respond as if you're commenting on Reddit:
human
Why does smoke from incense or cigarettes not (usually) set off smoke alarms?
gpt
Fire Alarm / Smoke Detector Manufacturer here.

Household smoke detectors (excluding Heat and CO) fall into two catagories, Ionisation and Photoelectric.

Ionisation smoke detectors (the detectors with the radioactive symbol on their label) are designed to detect sub-micron particals of combustion (different to thick smoke). Examples of sub-micron particles are cooking vapours (released from opening a hot oven, for example), vehicle exhaust, birthday candles, lighters, etc. Basically smoke that is the result of something burning, but you can't see. Ionisation smoke detectors in the house react well to fast, flaming fires (flash flame from a pot of oil on the stove, for example). 

Photoelectric detectors simple use an infrared transmitter and receiver in a chamber in the detector. As thicker, visible smoke enters the chamber, it blocks the light and the detector registers this change. When the smoke obscures the light to a certain level, the detector goes into alarm. Photoelectric detectors react well to visible smoke (cigarette, burning meat, smouldering natural fibres, etc).

To answer your question, it's very likely you have an Ionisation type installed, and it is not detecting sub-micron particulate in the air (as cigarette smoke is greater than one mircon and the ionisation detector cannot see it).

Please read this: The majority of household fires are caused by smouldering fires (burnt out motors, rats chewing electrical wires, cigatette left on bed or couch). These fires do not immediately show flame, but smoulder away and generate smoke for minutes (sometimes hours) before flaming. In this case, Ionisation detectors are not effective in providing early warning. Photoelectric detectors are far more suitable for this purpose. Please, when you check your battery next, check it's type. If it is a ionisation detector, please consider purchasing a photoelectric as a replacement.

TL;DR - Ion detectors (ones with radioactive symbol) can't see visible smoke. Photoelectric type detectors (stated on product label) do.