The main problem with copper is that it will precipitate out of solution, initially coloring the water green but also (possibly over a longer period of time) staining plaster. Though the solubility product of copper hydroxide implies that it should precipitate first, it does not due to soluble ion pairs (including neutral copper hydroxide itself). The data for actual solubility of copper hydroxide (which is blue -- see here) is inconsistent so instead I will focus on the solubility of copper carbonate (which is blue-green -- see here).
At standard conditions of pH 7.5, TA 100, CYA 40, CH 300, TDS 535, Temp 80F, the maximum copper concentration is 2.52 ppm. If one adds a shock level of chlorine to go from 3.5 ppm to 16.0 ppm FC, then the pH will rise to 8.14 and the maximum copper concentration drops to 0.56 ppm. So adding chlorine can make the water turn green and this is almost a sure sign of copper since adding chlorine, if at sufficient levels relative to CYA, usually bleaches any existing algae making it less green while with copper the pool will turn more green. Eventually as the FC level drops, the pH will drop as well and the copper will redissolve and the green will dissipate.
If one starts with a pH of 7.2, TA 93.4, by first adding Muriatic Acid (making the maximum copper limit is 5.3 ppm), then the chlorine addition will only raise the pH to 7.56 with a maximum copper limit of 2.19 ppm. So one way of avoiding green when there is copper while still being able to shock the algae is to lower the pH first. This also makes the chlorine more effective since the disinfecting chlorine concentration in the case above would be 0.243 ppm while first lowering the pH has the disinfecting chlorine concentration be 0.295 ppm.
The easiest way to know if green is from copper or algae is to see if there is any significant drop in FC level overnight. Algae will cause a drop in FC while copper will not. Also, if the water is clear but green and was not cloudy or dull previously, then this is more likely to be copper than algae. Sometimes, water can become cloudy first and then green and still not be algae. This would occur if already at calcium carbonate saturation, but adding more pH Up or Alkalinity Up which makes the water cloudy and then adding a copper-based algaecide which then makes the cloudy water turn green (this thread describes just such a situation).