Where did you read this as it isn't a listed side-effect? At very high doses well above its therapeutic dose range citalopram may affect the electrical system of the heart, but this is true of many medications, including quite a few heart meds. The only concern might come from taking a number of meds which have the same impact, but that is why meds have to be prescribed by a doctor. A major part of their job is taking such issues into account when selecting meds.
Anxiety can trigger such symptoms via several pathways, adrenaline surges; from the
enteric nervous system, the mini brain which controls the gut and to a considerable extent the brain, and also connects to and affects the heart and lungs via the vagus nerves; much more rarely through spasm of the main heart arteries during panic attacks. While unpleasant and scary these very rarely damage the heart (or any other organ).
Serotonergic antidepressants are mild anticoagulants which reduce the risk of having a heart attack, or ischemic stroke, although they may increase risks for the much less common haemorrhagic stroke.
There is evidence that serotonergic ADs can reduce cancer risk by, among other other means, stimulating the immune system to fight
some cancers
ADs typically take 3-12 weeks to kick-in with most beginning to see positive results around the 5-7 week mark. They have no direct effect on anxiety, or depression in the way say aspirin has on a headache. They work by stimulating the growth of
new brain cells (neurogenesis) to replace cells killed, or prevented from growing by high brain stress hormone levels. The therapeutic response is produced by these new cells and the stronger interconnections they forge, not the meds directly, and they take time to bud, grow and mature. For a more detailed explanation see:
How antidepressant drugs act.
As for side-effects (SEs), these may range from not having any to sometimes severe reactions, especially during the first couple of weeks due to the increased serotonin activity. While it is often promoted as a 'feel good' neurotransmitter, serotonin is anything but. After a few weeks the increased activity triggers the downregulation of serotonin synthesis and expression and any SEs usually begin to ease, but they may return for a while after dose increases. The thing to always keep in mind is that while unpleasant, they are rarely harmful. The best way of minimizing SE severity is by starting on a low dose, for citalopram no more than 10mg, 5mg may be even better, and ramping the dose up by the same amount at 7-8 day intervals <-get the prescribing physician's okay before doing this if s/he has recommended a different approach.